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COPYRIGHT DEPOSIT. 



THE 



New York Trade School'sTextbook 



ON 



Pattern Drafting 



SUITABLE FOR ALL WORKERS IN SHEET METAL 



This Treatise represents the Course of Instruttion provided by tlje 
New York Trade School in its Sheet Metal Department 



DRAWINGS AND TEXT PREPARED BY 

WILLIAM NEUBECKER, Instructor 



FIRST HDITION 



Copyrighted, iqos, by 
NEW YORK TRADE SCHOOL 



14 



Ms- 



LIBRARY of CONGRESS 

Two Copies Received 

NOV 24 1905 

Cooynem Entry 

~U^ a v / V tf 4' 

cuss tX XHc. NO, 

I 3 I 9 I 

COPY B. 



5" 



PREFACE 

In addition to the practical construction of metal cornices and skylights, and the 
preparation of patterns bearing on those branches, the Course of Instruction in the Sheet 
Metal Department of the New York Trade School is now enlarged to include pattern 
drafting for sheet metal workers in general. 

The course represented by this textbook comprises three divisions, namely: 

Part I. Parallel Line Developments. 

Part 2. Radial I^ine Developments. 

Part 3. Triangulation. 

All told, there are 235 exercises, and in arranging the course of study, heed 
has been given to the selection of problems of practical utility. The course covers, 
thoroughly and concisely, the principles which underlie pattern drafting, and, supple- 
mented by the verbal instruction imparted by the teachers, will enable the student to 
prepare the patterns for the usual forms arising in sheet metal work. 

Before entering upon the studies in this textbook, a short course in elementary 
geometry is provided. 



PRELIMINARY 

Each illustration shows how many times the problem is to be enlarged when drawn 
by the student. Thus (E 2x) means enlarge twice; (E 3x) enlarge three times, and so 
on. All drawings will then be of ample proportions to clearly show all points of inter- 
section, and to permit each step in the development of the pattern to be e;isily shown. 




The letters and numerals of the pattern need not be reproduced on the student's own 
drawing, unless he otherwise desires. 

Each plate must have marginal lines as illustrated in Fig. i, together with the proper 
lettering. The number of problems to be placed on each pl'ate, will be governed by the 
size of the respective drawings. Over the center of each drawing, the word "Problem" 
and its "Number" is to appear, the problems as developed being numbered consecu- 
tively by the student. At the bottom of the plate to the left, the student should place 
his name, and to the right, his class number. Have a space of Y' between all lettering 

-^c::name: class n° 

^ (full size) 

I Fig. 2. 

and the drawings. Letters and numerals to be drawn on an angle of 60°. Fig. 2 shows 
style of lettering desired. All the patterns illustrated are net. That is, no allowance 
has been made for a lap for the purpose of soldering, seaming or riveting. 

Before starting a problem, the text should be carefully read by the student, so as 
to acquire an intelligent conception of the drawing he is to undertake. 



PART ONE— PARALLEL LINE DEVELOPMENTS 

Under this head comes all patterns that can be developed by means of parallel lines. 
This method is one of the most simple that can be used in getting out the pattern of any 
form the opposite lines of which are parallel, such as piping, flaring ware with parallel 
bends, mouldings, skylights, etc. There are certain fixed principles that apply to develop- 
ments by this method, and they are set forth in connection with Fig. 3, viz.: 

1. There must be an elevation or plan ,4, showing the line of joint or miter line B C . 

2. In line with either the plan or elevation, the section or profile D of the article 
to be developed must be drawn, and if curved, must be divided into any convenient or 
equal number of spaces as shown from i to 10. From these points, lines are projected 
to the miter line, parallel to the lines of the article. 



DEVELOPMENT 




STRETCH-OUT LINE OR 
GIRTH 



Fig 3- 



3. At a right angle to the plan or elevation .4, draw the line E F. This is the stretch- 
out line or girth. Upon this line, reproduce the measurements i to 10. This gives, in 
the flat, the length of material required to bend the profile D. 

4. At a right angle to the stretchout line E F, and from points i to 10, erect measuring 
lines, which are then intersected by lines, drawn at a right angle to the lines of the article 
A, from similar intersections on the miter line B C. 

5. A line then traced through intersections thus obtained, as shown by E F H G, 
gives the desired pattern. 

It is immaterial what shape the section or profile may be ; or whether the merit 



6 THE NEW YORK TRADE SCHOOL'S 

line 5 C is straight, curved or irregular, the principle is similar in all cases. Suppose 
a b c d to be a zinc moulding, in shape similar to the profile D, and that a piece is cut 
from it with a saw, on the line B C. If the lower portion A is now drawn apart and 
flattened, the shape will be the same as the pattern E F H G. Thus it will be seen that 
the principles of parallel line development is to find the true girth, and on the measuring 
lines erected therefrom, place the various lengths obtained from the intersections on 
the miter line. 

While some of the problems appearing in Part One require also a knowledge of pro- 
jection, that subject will be explained when such problems are reached. 

PATTERNS FOR VARIOUS PIECED ELBOWS 

FIG. 4. Shows patterns for a two and three-pieced elbow, also for an elbow at any 
angle, all having the same plan or profile. 

First draw the elevation of the two-pieced elbow as shown hy A B C D E F. In 
line with one arm of the elbow, place the plan G, after which, draw the diameter 1-7. 
As both halves of the plan are symmetrical, divide the upper half only into equal parts 
as shown from i to 7. From these points, erect vertical lines, intersecting the mitej 
line C F as shown. Extend the line D E as shown by 'J K, and upon this line place the 
stretchout of the full plan, as shown by similar figures on J K. From these points, and 
at a right angle to J K, erect lines as shown, which intersect with lines drawn at a right 
angle to F E from like numbered intersections on the miter line C F. Trace a line 
through points thus obtained, then will 'J K L he the pattern for one of the arms of a 
two-pieced elbow. This method can be used for any pieced elbow, no matter what the 
angle may be. There is another method for getting out a two-pieced elbow having an 
angle of 90°, and the pattern can be developed without using the elevation or miter line, 
viz.: After the stretchout J K has been obtained, and knowing the length of the throat 
as K I , it is only necessary to place the profile of half the pipe on the line K i extended 
to 7, and as shown by H, and, dividing H into similar parts as G, horizontal lines are 
drawn, which intersect vertical lines drawn from J K, resulting in a shape similar to 
that obtained from the miter line. As previously stated, this loxle is applicable only 
to two-piece elbows, constructed at a right angle, and it does not matter what shape 
the pipe may have. 

The elevation of a three-pieced elbow is shown hy MNOPRST U and is drawn 
as follows: First draw the right angle M V P, and knowing the depth of the throat 
V R and the diameter of the pipe R P, use V as center, and draw the quadrants or 
quarter circles R U and P M. From P and R erect vertical lines, and from AI and L' 
draw horizontal lines, which arc to intersect lines drawn at an angle of 45° tangent to the 
two quadrants, thus obtaining the intersections A', 0, S and T. From N and draw 
the miter lines toward V as shown. Then F" R S and T U M N are each one half 



TEXT BOOK ON PATTERN DRAFTING 7 

oi N S T. From the various intersections in the plan G, lines (not shown) are erected 
until they intersect the miter line 5 0. From here, the same steps are followed as in 
the two-pieced elbow, and the pattern shown by W X Y is obtained. W X Y represents 
the pattern for both the top and bottom pieces of the elbow. By reversing the pattern 




Fig. 4. 



and tracing it opposite the line IT A', as shown by the dotted line, the pattern for the 
middle piece is obtained. No matter how many pieces an elbow may have, the pattern 
for either end is always one half the pattern for the other pieces. 

When an elbow must be made to fit a certain angle, the method of obtaining the 
miter line is as follows: Let .4' B' C be the desired angle. With B' as center and any 
convenient radius, describe the arc a b. With a and b as centers and a radius slightly 



8 THE NEW YORK TFL\DE SCHOOL'S 

larger than before, draw arcs intersecting at c. Then draw the miter Hne 5' c, and 
knowing the diameter of the pipe, draw the lines D^ E^ and E'- F' parallel to C 5' and 
B' A\ The pattern Z is then obtained in the manner already explained. 

When obtaining the patterns for pieced elbows, it is not necessary to draw the entire 
elevation to obtain the rise of the miter line, as was done in the three-pieced elbow. By 
a simple rule, and with the aid of the protractor, the rise of the miter line can be found, 
no matter what the throat or diameter of the elbow may be. If the pattern for a six- 
pieced elbow had to be laid out, the throat of which was 30 inches and diameter 20 inches, 
it would hardlv be practicable to first draw the full quadrant in order to obtain the rise 
of the miter line. Using the protractor as illustrated in Figs. 5 and 6, much time can 
be saved over the method shown in Fig. 4. As a rule, all elbows join together and form 
an angle of 90° no matter how many pieces they contain. The angle at which the elbow 
is to be connected, forms the basis by which the rise of the miter line is computed. 

FIG. 5. Shows a three-pieced elbow, which, when completed, should have an angle 
of 90°. As the middle section B equals twice .4, then 4 will be the divisor for 90. ^ = 
2 2 A. Thus the first miter line will have a rise or angle of 22^}°. As B = 2X^1, the second 
miter line will be drawn at an angle of 67^°. We then have 22^ -f- 45 + 22^ = 90. 
Therefore in all elbows of no matter what angle, the following rule should be followed, 
viz.: For each of the end pieces count i, and for each of the other pieces count 2. 




Fig. 5. 



FIG. 6. Illustrates how the protractor is used. Assuming that patterns are wanted 
for 2, 3, 4, 5, 6 and 7-pieced elbows, each having a throat measurement of 15 inches, 
and a diameter of 6 inches, the elbows when finished to have an angle of 90°, we would 
proceed as follows : Extend the line of the base of the protractor as shown by A C. Make 
.4 B 15 inches and B C 6 inches, and from B and C erect vertical lines of indefinite 
length. As a two-pieced elbow has but two end pieces and the angle when completed 
is to be 90°, then y^ = 45 or the degree at which a line must be drawn from the center 
.4 until it intersects the vertical lines of the pipe at D. This line will be the miter line 
for a two-pieced elbow. For a three-pieced elbow, the two end pieces count 2 and the 



TEXT BOOK ON PATTERN DRAFTING 9 

middle piece counts 2 which equals 4; "/ = 22^ or the degree at which a line will be 
drawn from A, as shown by .4 E. In similar manner, also shown in Fig. 6, we obtain 
the rise of the miter line for 4, 5, 6 and 7-pieced elbows. For example, a seven-pieced 
elbow is desired. The two end pieces count 2 and the other five pieces 10; 2 + 10 = 12 ; 






A 


D 


"^Z 




/ 


f 






..•h^>-^ 


E 




j^>^ 




-- 




F 

G 
H 
1 


B 




C 



THROAT 

Fig. 6. 



an ^ y^°^ which represents the angle of the miter line. If a four-piece elbow was to 
be made, having an angle of 30°, as shown by X, the same rule is employed. The two 
end pieces count 2 and the other two pieces count 4. 4 -|- 2 = 6 ; -\i = 5°, or the angle 
of the miter line, as shown. 



(E5X) 



A 
•z P. 










B 
3 P. 


a 




FIG. 7. Using the protractor by which to obtain the angle of the miter line, lay 
out the patterns for a 2, 3, 4, 5 and 6-pieced elbow, the respective profiles or sections 
being as per outlines ,4, B, C, D and E in Fig. 7. Each elbow to have a 6-inch throat 
and an angle of 90°. The patterns for the end pieces only are required, similar to IV X V 
in Fig. 4. 



lo THE NEW YORK TRADE SCHOOL'S 

FIGS. 8 and 9. Here is shown the method of drawing the elliptical figure when the 
length and width are given. These two rules appear in many text books, and are re- 
peated here because of their simplicity. If an ellipse is required with length equal to 
A B in Fig. 8 and width equal to C D, then take the distance from C to D and place 
it from B to a, and divide a A into three equal spaces, as shown by b c. With a radius 
equal to two spaces, and with E as center, describe the arcs on ^ B at e and d. With 





a radius equal to e d and with e and d as centers, describe arcs intersecting each other 
at i and /. Draw lines from i and /, through d and e as shown. Then i and / are the 
centers from which are drawui the arcs « and / m, and e and d the centers from which 
are drawn the arcs o I and n m. This ellipse is constructed from four center points 
and is of value in laying out flaring work when the centers, from which the arcs are 
struck, must be known. In the case of elbows, when the center points have no value 
and the ellipse is large, the figure can be constructed with string and pencil as illustrated 
in Fig. 9, in which half of A B is taken as radius, and with C or Z? as center, arcs are 
drawn on A B, as shown by a and b. At a and b stick two pins and make a loop around 
the pins wath a string, so that when the pencil draws the string taut, the pencil point 
will meet D. With the pencil in position, as shown at c, describe the ellipse, allowing 
the string to guide the pencil point. These methods of drawing the ellipse should be 
used in connection with the problems shown in Fig. 7. 



PATTERNS FOR VARIOUS INTERSECTING PIPES 

FIG. 10. Shows the intersections and patterns of a round and square pipe at right 
angles, the round pipe being placed over the angle of the square pipe. The profile of 
the square pipe is indicated in the end view hy A B C D, and in the side view, by 
E F G H. J and K show, respectively, the positions of the round pipes in both views. 
Above J and K in their proper positions draw the profiles of the roimd pipes as shown 
by L and L\ Divide both into equal spaces being careful that if i and 7 are at top 
and bottom in L, they will be at the sides in U, because each represents a different view. 
From the various points in L, draw lines parallel to the pipe 'J until they intersect the 



TEXT BOOK ON PATTERN DRAFTING ii 

sides B A and .4 D of the square pipe. From these intersections draw horizontal Hnes, 
which in turn are intersected by vertical lines drawn from similar points in the profile 
L', resulting in the miter line U V W. The pattern for the round pipe is obtained by 
drawing the horizontal line i° i', upon which, the stretchout of the full circle is placed, 
as shown. From the various points on i° i', drop vertical lines, which intersect by 
lines drawn from similar points on the sides B A and ^4 D. Trace a line, as shown 
hy M N 0, and the desired pattern is secured. To get out the pattern for the opening 
in the square pipe, take the stretchout of the various points on B A D and place them 
on F G, extended as 5' D^. Draw the measuring lines, as shown, at right angles to 
5' D', which intersect by vertical lines extended from similar intersections in the miter 
line U V W . Trace a line as shown hy P R S T, which gives the desired opening. 




Fig. 10. 



This opening can also be obtained from the end view as follows : At right angle to .4 D 
from the various intersections, project lines indefinitely as shown, and at a right angle 
to these lines draw a line as a-b. Then measuring from the line 4-10 in the profile 
L, take the various distances to jioints i, 2 and 3, etc., and place them on lines having 
similar numbers on either side of the line a-b. The shaded portion represents half of 



12 THE NEW YORK TRADE SCHOOL'S 

the opening. When sheet metal work is constructed from No. 20 to 30 gauge metal, 
it is not customary to allow for its thickness in the development of the pattern, but when 
heavier gauge than No. 20 is used, it is the practice to increase the stretchout. Some 
mechanics allow 3. 141 6 times the thickness of the metal, while others allow four and 
six times the thickness. The best practice is to allow seven times the thickness. What- 
ever the allowance may be, the rule for setting it proportionally throughout the stretch- 
out is as follows: Suppose the pipe J was to be constructed of i-inch metal, then 
J X i = li; the extra allowance to be placed on the stretchout line from i' to a' . Then 
using 1° as center and 1° a' as radius, an arc is struck until it intersects the vertical line 
at b' erected from i'. Draw a line from fc' to 1° and erect lines as shown. This divides 
h' 1° into equal parts, which line is then used the same as i' 1° in developing the pattern 
when heavy metal is to be used. When a complete circle is employed, seven times the 
thickness of the metal must be added to the stretchout. If a half or a quarter circle 
is employed, one-half or one-quarter of seven times the thickness is added to the stretch- 
out. Whatever the fractional part of the profile may be, similar fractional amount is 
added to the stretchout. This feature will be taken up as we proceed. 

FIG. II. Applying the method given in Fig. 10, develop the patterns for the T-joint 
in Fig. II, when the pieces A and B are at a right angle, also when A is at an angle 
of 45°, as shown at C. The method of obtaining the miter line on side is easily ascer- 
tained by refen-ing to like letters and figures in both views. 

FIG. 12. Shows a Y the diameter of each branch being the same. The miter line 
a ^ is obtained by bisecting the angle t a c by the line d e. A is the profile. 



a 

/ 




" 


"" 


Slsj^ 


c\ 


1 aJ 1 


(E5X) 


1 1 
1 1 




„^ 




1 


'^ 










" 


" 


\__J 



SICE 

Fig. II. 




Fig. 12. 



FIGS. 13 and 14. Show pipes of different diameters, the vertical pipe in one case 
being placed in the center and in the other to one side of the horizontal. Also at right 
angle and at an angle of 45°, as shown by the solid and dotted lines respectively. 

Note hoAv the miter lines on the side are projected. In the problems in Figs. 13 
and 14 where the intersections are at right angles to each other, the small and large 
pipes A and B in both figures are to be constructed from i-inch metal, and the patterns 



TEXT BOOK ON PATTERN DRAFTING 



13 



for the vertical pipes A are to be developed as shown in Fig. 10. In order that the 
method of allowing for the thickness of the metal in the opening in the horizontal pipe 
may be understood, the pattern for the opening in B in Fig. 14 has been prepared. Take 
the stretchout of 1-2-4-3 in end view and place it on a b as shown. As the smaller 
pipe intersects one-quarter of the circumference of the larger pipe, and assuming that 
i-inch metal is used, then take one-fourth of 7 X -i or -^^f,, and place it on a-b from 3 
to c. With I as center, draw the arc c 3', which intersect by a line drawn from 3. Draw 
a line from 3' to i, which intersect by a line drawn from 2-4. Take the stretchout 
of 3' b ami place it on d e as shown. Draw the usual measuring lines and obtain the 
opening shown by the shaded lines. In finding the opening in Fig. 13, measurements 





PATTERN 

FOR 

OPENING IN 

MAIN PIPE 

B 



(E5X) 


A 1 
!l 


c> 




•1 


w- 








B 



SIDE 

Fig. 14. 



are taken in the end view, to ascertain how much of the circumference is intersected 
by the small pipe, and if it be one-fifth, then one-fifth of 7 X i is to be added to the 
stretchout. 

FIG. 15. Shows the intersections between a rectangular and round pipe for which 
patterns are to be obtained in accordance with principles already explained. 



PATTERNS FOR PIPES INTERSECTING PITCHED ROOFS 

FIG 16. Shows the method of obtaining the patterns for the pipe and roof flange 
when the pipe passes through one side of the roof. .4 B shows the pitch of the roof, 
C the side view of the pipe and D its section. The section is divided into equal parts 
as shown, and the pattern E obtained in a manner similar to the development of elbow 



14 



THE NEW YORK TRADE SCHOOL'S 



patterns. To obtain the pattern for the roof flange, or the opening to be cut in the roof, 
draw lines at right angles to A B from the various intersections i to 5. On the line 
1-3 place half of section D, as shown by D\ which divide into equal spaces to corre- 
spond to D. From these points in D' draw lines parallel to .4 B, intersecting similar 
lines extended from A B. A line traced through the points as shown will be the desired 
opening. A more simple way of obtaining this roof opening is to use the method given 
in Fig. 9. The size of the flange required should be added around the opening just ob- 
tained in Fig. 16. 



(E4X) 




Fig. 15. 



Fig. 16. 



FIG. 17. When a pipe is to set over the four hips of a roof, the patterns are obtained 
as shown in Fig. 17. ABC shows the pitch of the roof, and D E F G the plan view. 
Draw the plan of the hips G E and D F. In this case an octagon shaft or tube is to be 
used as shown in plan by H and in elevation by -4 . As the pattern for one-quarter 
answers for all four sides, then number all comers and intersection at the hips alike, as 
shown by i, 2, 2, i, etc. From these points drop lines intersecting the pitch A C. From 
the intersections on A C, draw horizontal lines to meet lines drawn vertically from similar 
numbers in plan as shown, thus giving the miter line in elevation. This miter Hne is 
not necessary in developing the pattern, but is shown here to explain the method of 
projecting the miter line, no matter what shape the pipe, or what pitch the roof may 
have. The pattern for the octagon pipe is shown hy J K LM and is like similar develop- 
ments already gone over. To obtain the pattern for the opening in one side and the 
pattern for one side of the hip roof, take the stretchout of .4 i 2 5 in eleva- 
tion and place it at right angles to D E in plan as shown by A^ i 2 B\ Through these 



TEXT BOOK ON PATTERN DRAFTING 



IS 



points, draw vertical lines to intersect horizontal lines drawn from similar numbers in 
plan, resulting in the pattern shape shown. 

FIGS. 1 8 and 19. Show respectively a cylinder passing through a double pitched 
roof, and a cyHnder setting on a hipped roof. In each case the patterns for both cylinder 
and roof openings are to be developed. 




Fig. 17. 



ELEVATION 





Fig. ig. 



INTERSECTIONS BETWEEN VARIOUS SHAPED SHAFTS AND SPHERE 

FIG. 20. In ornamental sheet metal work it often happens that moulded shafts or 
mouldings will miter against a sphere at various angles. When the shape of the shaft 
is round or square, or the shape is such that each of the sides are symmetrical and the 
shaft miters directly over the center of the sphere, then the patterns can be developed 
as shown in Fig. 20, in which the sphere in plan is struck from A as center, and the 



i6 



THE NEW YORK TRADE SCHOOL'vS 



various arcs forming the shaft are struck from a, b. c and (/. With B as center, draw 
the elevation of the sphere. Then divide the quarter plan of the shaft as shown, from 
which points drop perpendicular lines intersecting the sphere in elevation at i, 2 and 3. 
From these intersections, carry lines at right angle to the center line, tnitil they intersect 
CD at i', 2' and 3'. Then, using B as center, with radii equal to Bi', B2' and B^' , draw 
arcs to meet \'ertical lines drawn from similar numbered intersections in the opposite 
quarter plan of the shaft, resulting in the miter line between the shaft and sphere, shown 




(E3X) 



by i', 2", 3", 2'" and i"'. In this problem, as well as in others which will follow, the 
line of intersection or miter line must first be obtained before the pattern can be 
developed. It is, therefore, important that the student bear in mind the method of 
projecting the miter line. After the miter line has been obtained, draw the stretchout 
line EF, upon which place the stretchout of one-quarter of the shaft in plan as shown 
by the duplicate numbers on EF. Draw the measuring lines in the usual manner, to 
intersect lines drawn parallel to EF from similar numbers'" in the miter line. Then 
EFHG is the pattern for one-quarter of the shaft. 



TEXT BOOK ON PATTERN DRAFTING 



17 



FIG. 21. When the shaft or moulding intersects the sphere to one side of its center, 
as in Fig. 21, the miter hne and pattern are obtained by means of horizontal planes 
drawn through the sphere. In this case the intersection is between a moulding placed 
at an angle of 45°, and a sphere. Draw the elevation of the sphere B, and at an angle 
of 45°, draw the outline of the moulding iLMg. Below the elevation draw the section 
of the sphere A, upon which, in its proper position, draw the section of the mould as 
shown. It will be noticed that the rear of the mould touches the center line of the 
sphere. With .4 as center and the bends in the mould as radii, draw the concentric 
semi-circles shown. Establish a few other points at pleasure so as to obtain intermediate 
points in the profile, and draw semi-circles as shown, intersecting the center line at o, 
h, c, d and e. These semi-circles then represent horizontal planes, which are projected 




into the elevation by drawing lines at right angle to ha in section until they intersect 
the sphere in elevation at a, b, c, d and c. From these intersections, lines are drawn 
parallel to LM as shown. As the points i and 3 in the section intersect the plane a, 
then project the points i and 3 until they intersect similar points in plane a in elevation 
at I and 3. In the same manner project points 2 to 9. Trace the miter line through 
points thus obtained in elevation as shown. The pattern is developed by extending 



1 8 THE NEW YORK TRADE SCHOOL'S 

the line LM, as CD, upon which place the stretchout of the mould in section, being 
careful to measure each space separately because they are all unequal. Measuring lines 
are now drawn and intersected as shown, resulting when traced in the pattern CDEF. 
As any plane section through a sphere is a circle, then it is evident that one-half of 
ih in section is the radius with which to complete the arc FG in the pattern. Therefore 
take one-half of ih as radius, and with F and G as centers, intersect arcs at in, which 
is the center point from which to get the arc FG. In similar manner find the center 
H, by using as radius one-half of jk in section. 

FIGS. 22 and 23. Applying the method given in Fig. 20, develop the patterns for 
the shafts shown in Figs. 22 and 23, representing a square and octagonal shaft, mitering 
over the center of a sphere. In these two problems, as well as the two which follow, 
all points of intersection have similar letters and numbers. 




Fig. 22. 




FIGS. 24 and 25. A round shaft placed t(.) one side of the center of a sphere is shown 
m Fig. 24, and in Fig. 25 a square shaft is set diagonally past the center of the sphere. 
Develop the patterns for each problem, following the method explained in connection 
with Fig. 21. The miter line in Fig. 25 is not completed, the three points of intersec- 
tions only being shown. These three points are all that is necessary in developing the 
pattern. The arcs between these points in the pattern are to be obtained by using one- 
half of de and /n' in plan as radius. 



PATTERN FOR FLARING PAN 

FIG. 26. When the pattern for a flaring pan is required, the corners of which are 
to be made watertight by folding together and turning them to the sides or ends of the 



TEXT BOOK ON PATTERN DRAFTING 



19 



pan, it is necessary to know how much must be notched from the corners, so that when 
folded they will come directly under the wired edge of the pan. This is accomplished 
in the manner illustrated in Fig. 26, the pattern being shown for a pan in which the 





Fig. 25. 



sides have more flare than the ends. L,et A BCD be the bottom of the pan. The end 
and side views are also drawn as shown, the vertical heights Fa and la' being the same. 
Thus EFGH is the end view, and IJKL the side. Extend AB as BM, which is made 
equal in length to FG in end view. Through M, parallel to BC, draw the line PU , which 
intersect by lines drawn from K and L in side ^-iew and at a right angle to PU . Connect 
the corners C to U and P to B. In similar manner extend CB as BN , which make equal 
In length to IL in side view. Through A' draw the line 1 '0, which intersect by vertical 
lines drawn from H and G in end \-iew. Draw VA and BO. Trace similar miters on 
opposite side and end as shown. Then will VOPUTSRiABCD be the pattern for the 
pan if the comers were to have a raw edge. It will be noticed that the miters OB and 
BP have different angles, but have similar lengths as shown by the arc OP, struck from 
B as center. Assuming that the comer is to be turned towards the end of the pan, then 
bisect the angle OBP, obtaining the line of bisection hB. Now with of the end miter 
as center and with a radius less than would touch bl>, draw the arc cd. intersecting OB 



THE NEW YORK TRADE SCHOOL'S 



at e. With c as center and ec as radius, intersect cd at d. Draw a line from through 
d, meeting hB at /. From / draw a line to P. Then OfP is the amount to be notched 
from the comer, when it is turned towards the end. When the corner is to be tumed 
towards the side, the operations are similar, excepting that i is used as the center in 

H " G 




PLAN OF 
BOTTOM 



FULL PATTERN 




transferring the angle ijm. By referring to the various letters, the operation is easily 
followed. 

FIG. 27. Shows two other styles of pans. A is to have equal flare all around, while 
B will have no flare, the bottom of the pans to be square. 



ELEVATION 



(E3X) 



(E8X) 



Fig. 



TEXT BOOK ON PATTERN DRAFTING 



PATTERN FOR TRANSITION PIECE 

FIGS. 28 and 29, The former shows the rule for oljtaining patterns in piping when 
the lower pipe, in passing up, has to fall over and twist one-quarter way around to pass 
through given points. The principle is similar to Fig. 26 in the mitering of unequal 
flares. Thus in Fig. 28 NO PR is the lower pipe, which is to turn in the position shown 
hy JKLM. The front view is shown by ABCD and the side view by EFGH. EF in 
side view represents the measurement of material required for the side i in plan, DC 




Fig. 28. 



in front for side 2, HG for side 3 and AB for side 4. Having the plan, front and side 
views drawn in their proper positions, the patterns for sides i and 3 in plan are obtained 
as follows: Draw any vertical line as £'G"', upon which place the stretchout of EF and 
HG in side view, as shown respectively by E^F'- and H^G\ From these points draw 
lines at a right angle to E^G\ which intersect by lines drawn from corresponding points 



2 2 THE NEW YORK TRADE SCHOOL'S 

in plan. Trace lines through the various points obtained. Then will 7'A''0W' and 
M^UP^R^ be the patterns for the sides, having similar letters in plan. In a like manner 
obtain the patterns for the sides 2 and 4 in plan, as shown by the patterns marked 2 
and 4. When these transition pieces are large they are gotten out in four separate parts 
and double-seamed at the corners. If the size is such that they can be conveniently 
made from one piece of metal, then "the various patterns are joined, as shown in Fig. 29. 





Fig. 29. 



Fig. 30. 



FIGS. 30, 31 and 32. Are three problems to be solved according to the principle 
given in Fig. 28. Fig. 30 shows a transition piece, the base of which is oblong and top 
square, the vertical height a being equal. Fig. 31 shows an offset with equal dimen- 
sions at top and bottom. Fig. 32 shows similar pipes crossing each other. Each side 
is to be developed separately and then joined in one full pattern as shown in Fig. 29. 





Fig. 22. 



PATTERN FOR SCALE SCOOP 

FIGS. 33 and 34. When developing patterns for various shaped scoops, the parallel 
line method should be employed. Under this method the various shapes are cut from 



TEXT BOOK ON PATTERN DRAFTING 



23 



a cylinder or part of a cylinder as shown in Fig. ^t„ AB representing the cylinder and 
C and D scoops of different shapes cut from same. In the scoop C, the miter line takes 
up hut part of the cylinder. Fig. 34 illustrates how the pattern is obtained. First 




'•"i<:. ,1,^ Fig. 35 

draw the ele\-ation of the scoop as shown by A BCD and extend CD as CF. At a right 
angle to CF, from any convenient point, draw the line FE, upon which at pleasure estab- 
lish the center point H, so that FH will be the required radius with which to draw the 
arc JFK. As both halves of the section are symmetrical, then divide one-half into equal 
spaces, from which points and parallel to CD, draw lines intersecting the outline DB 
and miter line BC. At a right angle to CD draw the stretchout line LM upon which 




Fig. 34. 



the full stretchout is placed as shown. The pattern NOPR is then developed in accord- 
ance with the principles with which the student should now be familiar. 

FIG. 35. Shows a hand scoop. The section is a full circle from a to h and an irreg- 
ular curve from a to c. Full patterns are required. 



24 THE NEW YORK TRADE SCHOOL'S 



PATTERN FOR PIPE INTERSECTING ELBOW MITER 

FIGS. 36 and 37. When a branch must be taken from the angle of an elbow, the 
rule to be employed is shown in Fig. 36. It does not matter what size the branch or 
elbow may have, or how many pieces the elbow contains, or whether the branch is placed 
in the center of the elbow or to one side, the principle explained applies in each case. 

Let A, in plan, represent the center from which the circle 5, C, i, 5 is struck, being 
the profile of the elbow shown in elevation by KLHG, Ji' representing the miter line 
of the 45° angle. Draw the plan of the branch in its desired position as shown by 
iZ?£5 ; also its profile shown by F. Assuming that the center line of the branch in 
elevation is to fall upon the corner i', at an angle of 90° to the line of the elbow Li', 
draw the line I'l indefinitely, upon which establish the center F', and draw the profile 
in size equal to F in plan. Divide both of the profiles F and F' into the same number 
of spaces, being careful that if i and 5 represent the sides of the branch in plan, they 
will be placed in their relative positions in elevation. Parallel to the line 5-£ in plan 
and from the various intersections i to 8 in F, draw lines intersecting the circle A at 
I, 2-8, 3-7, 4-6 and 5. From these intersections draw vertical lines intersecting the 
miter line ^i' as shown, from which points parallel to I'L, draw Hnes indefinitely. Now 
from the various intersections in the profile F' parallel to i-i', draw lines intersecting 
similar numbered lines drawn from the plan, resulting in the points of intersections shown 
in elevation by i', 2', 3', 4', 5', 6', 7' and 8'. Trace the curved line of intersection from 
4' to 3' to 2' to i' to 8' to 7' to 6' to 5'. It is evident that before a hne can be traced 
from 5' to 4', the point of intersection b must first be found between the branch and 
the miter line Ji' . To find this point it is only necessary to assume that the portion 
of the elbow KJi'L is a straight cylinder, on to which the half profile F' from i to 5 
is to be mitered. Therefore extend the line ed (which represents the line taken from 
the point 5 in plan) indefinitely, which intersect by a line drawn from point 5 in the 
profile F', and obtain the intersection 5". Then trace a line from 4' to 5"-, intersecting 
the miter line Ji' at h, the desired point. From b, parallel to the branch, draw a line 
intersecting the profile F' at b' ; also drop a vertical line, intersecting the plan A at b" . 
These points will be used when developing the patterns. Trace a line from 4' to b. It 
is also evident that the line from b to 5' must be curved, as the profiles of both pipes 
are circles. Therefore at pleasure, establish on the line GH in elevation between the 
points 5' and b any point as a, through which draw the vertical line intersecting the plan 
A at a' . From this point, parallel to 5F, draw a line intersecting the profile F at a". 
^ake the distance from 5 to a" and place it from 5 to a" in the profile F\ from which 
point, parallel to the lines of the branch, draw a line intersecting similar line at a'" . 
Draw a line from b through a'" to 5', which completes the miter line between the branch 



TEXT BOOK ON PATTERN DRAFTING 



25 



and elbow. In the illustration the patterns are only shown for the openings to be cut 
from the elbow patterns ; but in drawing this problem the student is to develop the full 
patterns for the various pieces with seam at B in plan. To obtain the pattern for the 
opening in JGHi', extend the line GH as HM, upon which place the stretchout of the 
necessary spaces in 5-1 in plan .4 as shown. Erect vertical lines from HM, which inter- 
sect by horizontal lines drawn from similar intersections in elevation. Trace a line 




Fig. 36. 



through points thus obtained, then PON or the shaded portion is that part to be cut 
out of the full elbow pattern to admit the mitering of the branch. In similar manner 
obtain the opening for the piece JKLi'. At right angle to JK draw the line RS, upon 
which place the stretchout of the rec[uired spaces in that portion of the plan .4 shown 
from b" to i. Draw perpendicular lines from SR, which intersect by similar numbered 
lines drawn from the elevation at right angles to JK. TUV or the shaded portion is 



26 THE NEW YORK TRADE SCHOOL'S 

the desired opening. To avoid a confusion of lines, a tracing of the branch ir.Vs'V, 
with the various intersections, has been placed horizontally in Fig. 37. This pattern is 
obtained by drawing the vertical line AB upon which the stretchout of the profile F' 
in Fig. 36 is placed, as shown in Fig. 37. Horizontal or measuring lines are drawn, 
which are intersected by vertical lines drawn from similar numbered intersections in 
WY, resulting in the pattern CDE. 




Fig. 37. 



FIG. 38. Shows the intersection between a rectangular pipe and elbow, both of 
which are to be developed full. 



PATTERN FOR STATIONARY AWNING 

FIG. 39. In this figure ABC represents the elevation of a semi-circular window, on 
which is to be hung a stationary sheet metal awning, the latter to be constructed of 
^-inch metal. The semi-circle from 4 to 4 is struck from D as center, the sides 4-B and 



TEXT BOOK ON PATTERN DRAFTING 27 

4-C being straight. EFG shows the side view, the distance FG being estabUshed at 
pleasure. Having the front and side in their proper position, divide the profile BAG 

ELEVATION 



IV y 




' \ \ \ , 


Ji\.a 





"i"l 1 !"' 






12 3 3 1 

(E4X) 


y^ -^nLI 


1 1 


/ 'i 






2— 


3 


V i 


r 


-- 


J— - 


1 



F_AN 

Fiu. 38. 



into equal spaces as shown, and draw horizontal lines until they intersect EF, from 
which intersections, parallel to EG, draw lines indefinitely cutting FG as shown. From 




5 4 3 2 1 2 3 4 
ALLOWANCE FOR HEAVY 
METAL 



Fig. 39. 



any convenient point as H, at a right angle to EG draw HJ. Now measuring from the 
line AK in elevation, take the various distances to points i to 5 and place them on lines 



28 THE NEW YORK TRADE SCHOOL'S 

having similar numbers, measuring on either side of the hne HJ. A hne traced from 
5 to // to 5 will be the' true section through FK, from which the stretchout is obtained 
with which to develop the pattern. As the awning is to be made from i-inch metal, 
allowance for the thickness of the metal must be added to the stretchout, the manner 
of doing this being explained in connection with Fig. lo. Therefore in Fig. 39 draw 
any horizontal line as ad, upon which place the stretchout of the true section 5/^5, as 
shown by similar figures on ad. As seven times the thickness of the metal should be 
added to the stretchout for a full circle, and as we have but a half circle 4A4 in eleva- 
tion, add one -half of seven times -J-inch or y^-inch, as is indicated by 5-17 on the line ad. 
With d as center and da as radius, draw the arc ab, which intersect by the vertical line 
drawn from 5. Draw a line from 5 to d, also vertical lines from the points on ad, inter- 
secting hd as shown. Then will the various divisions on bd be the required stretchout, 
which transfer to line LM drawn at right angle to EG in side view. Measuring lines 
are now drawn and intersected in the usual manner and as shown in the drawing. 

FIG. 40. In this figure, A shows the elevation of a can lip, the plan view of which 
is cde. A true profile or section must be found through a-b. The lip is to be constructed 
from No. 24 iron, and no allowance is necessary for the thickness of the metal. 



ELEVATION 




(E6X) 



I \ 


c }_ 




t) 






-i 



F.ND SIDE 

Fig. 41. 



FIG. 41. Shows how the parallel line method can be employed for developing the 
gusset sheet a-b-cd, when the horizontal widths through ad and be are equal. Here 
jeih is the section through am and teih, the section through bti. Prepare the pattern 
for that portion shown by abed, a true section being required through ni'd. The gusset 
sheet is to be constructed from i-inch metal, and follow the rule given in Fig. 39. 

FIGS. 42 and 43. Are to be constructed from No. 24 metal and no allowance is 
required for the thickness of the metal In Fig. 42 BC is the plan of the can struck from 
A, and 3-4-5-6 the plan of the boss, the section of which on 4-5 is the diameter of the 
faucet shown at D. The true section is shown at E. The pattern for half of the boss 
is to be developed, with a seam as shown at top and bottom. Fig. 43 shows the plan 



TEXT BOOK ON Px^TTERN DRAFTING 



29 



and elevation of a tub with a flaring head, the width at top and bottom being equal. 
Only the pattern of abed is to be developed. 




Fig. 42. 



PATTERN FOR TWISTED CURVED ELBOW 

FIG. 44. Shows the plan and elevation of an elbow curved in both views. The 
horizontal section through 1/ in elevation is shown by i"f'f"i"' in plan, while the ver- 
tical section through $'"6" in plan is shown by 5-6-6'-3' in elevation. The curves in 
plan and elevation are struck from the centers Y and A' respectively. While a com- 

(E4X) 



ELEVATION /'' ^^y/ | 


r(| 




i 1 
1 1 


1] 

PLAN 1 
1 

1| 


-4 


i^ 



Fig. 43. 



pleted elbow of this kind appears like a complicated piece of pattern work, its development 
is very simple. Having drawn the plan and elevation in their proper positions, either 
one of the curves in plan or elevation can be divided into equal spaces (in this case the 
top curve .4j, as shown by the small figures i to 6. From these points vertical lines are 
drawn, intersecting the curves B, C and D, as shown by similar letters and figures. 
Establish an intermediate point in the curve B at e, another in the curve C at li ,and 
one in the curve D at D. Draw vertical lines through these points into the plan and 



3° 



THE NEW YORK TRADE SCHOOL'S 



elevation as shown. It will be noticed that in place of dividing each curve into equal 
spaces, only one curve (A) has been so divided, making all the other spaces in the curves 
B, C and D unequal. This method avoids a confusion of lines, and only necessitates 
placing each space separately on the various stretchouts as will be explained. There- 
fore, to obtain the pattern for the top A, draw any horizontal line as EF, upon which 
place the stretchout of the top curve A, as shown by similar figures on EF. At a right 



ELEVATION 




angle to EF, through the small figures, draw the usual measuring lines, which intersect 
by horizontal lines drawn from similar numbers in the plan, resulting in the pattern for 
top A. The portion shown by 5-6-5° is a reproduction of 5"'-6"-5" in plan, and is ob- 
tained by using 6"Y as radius, and then with 6 in the pattern for top as center, inter- 
secting the line 61' at a. Using the same radius, with a as center, draw the arc 6-5°. 
In precisely the same manner the pattern for the bottom B is obtained. Measure the 
various spaces in the curve B and place them on the stretchout hne G'H. Draw the 
usual measuring Hnes and intersect same as before, b being the center from which to 
draw the arc 6-5°. To obtain the patterns for the back C and front D in plan, take 
the stretchouts of the curve C and cun-e D, and place them on the horizontal lines I J 
and KL respectively. Draw the usual measuring lines, which intersect by lines drawn 
from similar numbered intersections in elevation, parallel to the stretchout lines, re- 
sulting in the patterns shown. i"f'i° and i"'f"i° are reproductions of i/i' in elevation, 
the radii cf and df" being obtained from Xf in elevation. 

FIG. 45. Shows the plan and elevation of an elbow, the horizontal and vertical 
sections of which are shown respectively by abed in plan and abed in elevation. 



TEXT BOOK ON PATTERN DRAFTING 



31 



PATTERNS FOR FACE MITERS 

FIG. 46. Shows the elevation of a panel, the comers of which are broken on the 
one end, thus forming outside miters at ab and //, and an inside miter at 
cd, the other end being circular, struck from the center .4. The shaded portion 
indicates the section of the panel mould. It will be noticed that the miter 




Fig. 45. 



ines of the in and outside angles are perfectly straight, as shown by one of 
the miter lines cd, while the miter line between the straight moulding DE and curved 
moulding Eh is an irregular line as shown by EXF. To obtain the miter line EF, take 
the vertical distances of 2, 3, 4 and 5 in the section, and place them on the horizontal 
line BC as shown by hfwe. Then using .4 as center, draw the various arcs intersecting 
similar numbered horizontal lines as shown. For the pattern for DEFG, place upon 
the stretchout line JH, the stretchout of the mould i to 6 as shown. Draw 
the measuring lines at right angle to JH, which intersect by lines drawn at right angle 
to DE from similar points on the miter lines DG and FE. resulting in the pattern shape 
LMNO. OL is the outside miter for the exterior angles shown in elevation, while the 
reverse of OL or the cut belonging to the dotted lines is the inside miter for the interior 
angles. Take the distance of ic or ca: or jd or db, and place it as shown by OP and LR 
and draw from P to R s. duplicate of the cut OL. Then OPRL is the pattern for icdj 
or cabd. To get the pattern for mnij, take one-half of mj and place it as shown from 
R to S and draw the vertical Hne ST. Then TPRS is the half pattern. The patterns 
for the circular mould will be explained in Part Two. 



32 



THE NEW YORK TRADE SCHOOL'S 



FIGS. 47, 48, 49 and 50. In Fig. 47 the patterns for a and b are to be developed. 
In Fig. 48 a triangular raised panel is to be drawn, the three sides of which are equal, 
as shown by the dotted curves, a-b is the section through cd. The center point c is 




C- - 



w' elevation 

Fig. 46. 



obtained by dropping the vertical line jd and intersecting it by a line drawn from the- 
apex h at right angles to ji. All three being alike, the pattern for e only is required 





Fig. 47. 



Fig. 48. 



Fig. 49 shows another form of face miters in the style of a pediment in a cornice. After 
the elevation A BCD has been drawn, draw the vertical miter line HI, and find the miter 
line F'J by bisecting the angle AFH by the line a-b. Place the profile E in position and 



TEXT BOOK ON PATTERN DRAFTING 



33 



proceed as shown by the dotted Hnes. Only the pattern for FHIJ is to be developed. 
Fig. 50 is another form of face miter, where a horizontal moulding AD joins a circular 
moulding BC. The vertical heights on a-b are placed on BC, and with F as center, 
arcs are drawn as explained in Fig. 46, resulting in the miter line GH in Fig. 50. The 
pattern for AGHD is to be developed. 




(E4X) 



Fig. 49. 



PATTERNS FOR RETURN MITERS 

FIG. 51. Shows the long and short method of obtaining a square return miter, also 
for obtaining return miters at any angle. Let A represent the elevation of a moulding, 
and B the plan of the in and outside miter. The long method of obtaining a square 
return miter is shown by EDGE. The mould A is divided into equal spaces and from 




Fig. 50. 



the points vertical lines are drawn to the miter line a-b in plan. The stretchout of the 
mould .4 is now placed upon the horizontal line ED, from which measuring lines are 
drawn and intersected by lines drawn from similar points on the miter line ab, parallel 
to ED. EDFG is the pattern for a square return miter. This same pattern can be 
obtained without the use of a plan, but the rule can only be employed for square miters, 
or 90° angles. At right angle to the line of the moulding A erect the stretchout line 



34 



THE NEW YORK TRADE SCHOOL'S 



LM, upon which the stretchout of the profile A is placed. Measuring lines are drawn 
and intersected as shown, resulting in the pattern shape LMNO. Upon comparison, 
the two patterns will be found alike. Should an inside square miter be required the 




Fig. 51. 



opposite cut of the outside miter is used, as shown by the dotted portion P. This 
is self-evident, because if we take that portion shown by T in plan, and place the miter 
line fe against the miter line ab, it will form one continuous mould, as shown by the 
dotted portion T'. 



TEXT BOOK ON PATTERN DRAFTING 



35 



The principle used for obtaining a square return miter by the long method, can 
also be applied to getting out patterns for return miters at any angle. Let C be the 
plan of the mould at any given angle. Find the miter lines cd and hi, and having the 
profile of the mould in its proper position, it is only necessary to drop lines inter- 
secting the miter line cd, when the pattern is obtained as shown by HIJK. For the 
inside miter hi in plan, the opposite cut of JK in pattern is all that is required, as 
shown by R, because if ihS is placed on the miter line cd, a straight mould is the result 
as shown by the dotted part 5'. No matter what profile or angle is required, these prin- 
ciples hold good in all cases. 

FIG. 52. In this figure, .4 is the profile of an eave trough, for which square in and 
outside miter patterns are to be developed by the short rule, placing the patterns above 
the section. The in and outside miter patterns are also to be obtained for the angle 
shown by abc in plan. 



ELEVATION 





Fig. 5^. 



Fig. 53. 



PATTERNS FOR ARTICLES WHOSE BASES ARE REGULAR POLYGONS 

FIG. 53. The princijilcs explained in the prcceeding problem are also applicable 
to regular polygons. In Fig. 53, A shows the elevation of a cap, the plan of which 
B is a hexagon. Draw the miter lines in plan as shown. Divide the profile in elevation 
into equal spaces, and extend vertical lines cutting the miter lines cic and be in plan. 
At right angle to ab draw the stretchout line CD, and proceed to develop the pattern 
in the usual manner. 

FIGS. 54, 55. The former shows the elevation and plan of a ball to be made in 
ten sections. In developing a pattern for a ball constructed in gore sections, it is 



36 



THE NEW YORK TRADE SCHOOL'S 



always best to first draw the plan, making ba the semi-diameter of the required ball, 
and then in line with ad construct the elevation. In developing patterns for any article, 
the bases of which are regular polygons, the student should bear in mind that the true 
profile must always be placed on a line at right angles to one of the sides in plan as ad, 
and not at right angles to the miter line ab. The pattern for one section abd is all that 
is required. Some times it is necessary to make a finished elevation, showing the 





(E4X) 



miter lines, and while this is not necessary in developing the pattern, the principle 
will be explained. From the various intersections in the half ball, drop lines to the 
miter line ab, from which points, parallel to ac, draw lines intersecting cb. From these 
points lines are erected, intersecting similar horizontal lines in elevation, as shown by 
the inner curved line. In Fig. 55 is shown an urn, the plan of which is an octagon. 
Make a finished elevation, showing the miter lines projected from the plan and develop 
the pattern for side A. 



PATTERN FOR ELBOW JOINING VERTICAL ROUND PIPE 

FIGS. 56, 57, 58 and 59. When pieced elbows are to be joined to round square 
or rectangular pipes, whether the pipe is in a vertical or horizontal position, or whether 
the center of the elbow is in line with the center of the pipe, as shown in plan in 
Fig. 56, or placed to one side, the principles here given are applicable to all. Let 
ABCD represent the elevation of the vertical pipe, DE the throat and DF the dia- 



TEXT BOOK ON PATTERN DRAFTING 



37 



meter of the elbow. Erect the vertical line EG and with E as center and ED as radius, 
draw the quadrant DH. As the elbow is to have four pieces, and as each of the 
middle sections represent two end sections, then divide the quadrant into six equal parts, 
making He and aD each equal to one part, and ab and be each equal to two parts. 
From E, through a, b and c, draw the miter lines af, be and cd and complete the out- 
line of the elbow DFGH. Draw the profile of the elbow as shown at J, dividing it 
into equal parts as shown from i to 7. In its proper position draw the plan of the 




Fig. 56- 



round pipe K. As the center of the elbow is to meet the center of the pipe, place a 
duplicate of the profile J in elevation, as shown by J^ in plan. If the line 4-4° is 
vertical in elevation, it must show horizontal in plan. Through the small figures in 
y draw horizontal lines until they intersect the profile K as shown, from which inter- 
sections erect lines indefinitely. Through the small figures in the profile J in eleva- 
tion, draw horizontal lines until they intersect the miter line de, from which points 
parallel to de, draw lines intersecting similar numbered vertical lines erected from the 



38 THE NEW YORK TRADE SCHOOL'S 

plan, as shown by 4, 3-5 and 2-6, allowing the balance of the lines to intersect the 
miter line be as shown. From the intersections on the miter line be, parallel to ej, 
draw lines intersecting similar vertical lines drawn from the plan. Through points 
thus obtained, trace the line in section 1', as shown from 4 to 3-5 to 2-6 ; and in 
section Z, a line from 4 to 3-5 to 2-6 to 1-7. It is evident that a straight line should 
not be drawn from the intersection 2-6 in section Y to 1-7 in section Z, it being neces- 
sary to first find the point of intersection, where the joint line between the elbow and 
vertical pipe crosses the miter line be of the elbow. This point can be found by 
assuming that the section Y of the elbow is a straight pipe intersecting the vertical 
pipe at the angle shown. Therefore, extend the line ni until it intersects the line drawn 
from I in plan at 1° in elevation. Trace a line from 2-6 in section F to 1°, which cuts 
the miter line be of the elbow at h, giving the desired point. Trace a line from // to 1-7 
in section Z. Then 4/^4 is the line of joint between the elbow and pipe. Drop the 
point /; in elevation, into the plan K as shown by /; and /;. Also project this point h 
in elevation parallel to the elbow ed and dG until the intersections /; and h' are obtained 
in the profile J. These points will be used in developing the patterns. Notice that 
the portion of the elbow shown dotted is not recjuired. To obtain the pattern for the 
opening to be cut in the vertical pipe, take the stretchout of all the spaces contained 
in 1-4-7 iri plan, and place them on the horizontal line AB in Fig. 57, as shown by 
similar numbers. From these small figures erect vertical lines as shown. Now, meas- 




uring in each instance from the line DC in elevation in Fig. 56, take the various 
vertical heights to the intersections 4, 3-5, 2-6, 1-7, /;, 2-6, 3-5 and 4, and place them 
on similar vertical lines in Fig. 57, measuring from the line AB, resulting in the pattern 
shape, when a line is traced through points thus obtained, as shown by h'^'h"^". The 
pattern for the section A' in Fig. 56 is obtained along the lines previously explained. 



TEXT BOOK ON PATTERN DRAFTING 



39 



To get the pattern for section Y, draw any vertical line as ic in Fig. 58, upon which 
place the stretchout of the profile J in Fig. 56. Draw the measuring lines in Fig. 58 
at right angles to u. From c in Fig. 56 draw the line ci at right angle to de. Now, 
measuring from this line, take the various distances to the various intersections on the 
miter hnes dc and 4/16, and place them on similar hnes in Fig. 58, measuring on either 





Fig. 58. 



Fig. 59. 



side of the line ic, giving the pattern shown. As the pattern for section Z in Fig. 56 
only requires the stretchout of J from h to 4° to //', place the stretchout upon the ver- 
tical line mh in Fig. 59 and obtain the pattern in a manner already explained, measuring 
from the line bm in Fig. 56 to the various intersections on the miter lines lib and ha. 

FIG. 60. Shows the intersection between a four-pieced elbow and rectangular pipe. 

Note that the intersection a is obtained by drawing a line from 4 to 5°, and the 
intersection b, b}' drawing a line from 2 to 3°. The intersections a and b are both pro- 
jected into the plan and profile in elevation as shown. The patterns are to be devel- 
oped for sections .4 and B of the elbow, and for the opening in the side C of the vertical 
pipe. 



4° 



THE NEW YORK TRADE SCHOOL'S 



PATTERNS FOR REDUCED MITERS 

FIG. 6i. The principles given in Fig. 6i for obtaining the patterns for a square 
reduced miter, are applicable to any reduced miter, no matter what shape it may 
have in either plan or elevation. Let CDEFGH be the plan of the reduced miter. 




Fig. 6o. 



The section at right angle to DE is shown by A. Divide this profile into convenient 
spaces and from these points project lines to the miter line DG, from which vertical 
lines are erected indefinitely. At right angle to CD from any convenient point as b, 
draw hi. Now, measure the various distances from the line ai in >1 to points i to 7 
and place them on similar lines, measuring from 16 in the profile B, thus obtaining the 
profile B, which is the section through HC in plan. It is evident that the height of 
the moulding remains the same, but the distances in plan EF and HC are unequal. 
The pattern for DEFG is obtained by placing the stretchout of A on FJ and proceed- 



TEXT BOOK ON PATTERN DRAFTING 



41 



ing in the usual manner. The pattern for CDGH is developed by placing the stretch- 
out of B on HL. 



L 70 




Fig. 6r. 



FIGS. 62, 63, 64 and 65. In Fig. 62, .4 is the given profile through a-b. The angle 
of the plan is an octagon and the true profile through C and the patterns for B and C 
are to be developed. Fig. 63 shows the plan and elevation of a cap, the patterns for 
A and B to be developed. Fig. 64 shows a moulded base, the bottom of which is an 





octagon and top abed square. Develop the patterns for the side A and gore piece B; 
also project the miter line ef from plan to elevation. Fig. 65 shows the soffit plan and 
elevation of the bottom of a bay window. In this problem the profile through A is 



42 



THE NEW YORK TRADE SCHOOL'S 



given and it is necessary to find the true profiles through B and C, at right angles to 
their face lines, after which the patterns are to be developed for A, B and C. The miter 
lines should also be projected from the plan to the elevation, although this is not neces- 
sary in the development of the patterns. In practice only one-half of elevation and 
plan is necessary. 




ELEVATION 




.^\\^'|S:'^y^^^^y■^t^■^V^K\\^k^^\^^\>^ 



(E4X) 



Fig. 64. 



Fig. 65. 



PATTERN FOR ROOF DORMER 

FIG. 66. Shows the elevation and side view of a roof dormer. The roof or top DE, 
instead of being on a horizontal line, has an incline and butts against the main roof FE. 
If the roof DE were horizontal, the problem would present nothing more than a butt 
miter and the true profile would be shown by the elevation ABC. But as the roof 
DE is inclined, a true profile must first be found through DH before the pattern can 
be developed. First draw the elevation ABC, using a, b and c as centers from which 
to strike the arcs ABC. Also draw the side view DEF, showing the dormer and main 
roofs at their proper angles, and divide the half elevation BC into equal spaces, as shown 
from I to 6. From these points draw horizontal lines, cutting the face of the dormer 
DC in side view from i to 6. From these intersections parallel to DE, draw lines cutting 
the main roof line FE also from i to 6. From D, at right angle to DE, draw the line 
DH intersecting the various Hues drawn from i to 6, and extend DH until it intersects 
the line drawn from point 6 parallel to DE at H. Now, take the various divisions on 
DH and place them on the center line extended in elevation as D^H\ from which points, 
horizontal lines are drawn and intersected by lines drawn at right angles to AC, from 
similar numbered points in the half elevation BC. Trace a line through points thus 
obtained, then D^JW will be the half true profile through DH in side view. Take a 



TEXT BOOK ON PATTERN DRAFTING 



43 



stretchout of this profile D^J, and place it on the line LK, which is drawn at right angles 
to DE. Through the small figures and at right angles to LK draw the usual measuring 
lines, which in turn are intersected by lines drawn at right angles to DE, from similar 
numbered intersections on the roof line EF and the face fine CD. MNO then repre- 
sents the half pattern for the dormer roof. Some times it is necessary to find the shape 
of the opening to be cut in the main roof. This is accomphshed by drawing F'£' 
parallel to FE and at right angle to FE, from the various intersections, i to 6, draw lines 
indefinitely, crossing F^E^ as shown. Then measuring in each instance from the center 
ine Ba in elevation, take the various horizontal distances to points i to 6 in BC, and 



HALF p;XTTLr!N 






FOR 






DORMER ROOF 




N 


\L 




7, 






i\ 


^"'"^ \' 


/ 


\ \ 


'^"^'^A 


\ 


\ \ 
\ \ 
\ \ 




(E4X) 



ONE HALF 

true profile 
through dh 

Fig. 66. 



HALF PATTERN 
FOR OPENING 
IN MAIN ROOF 



place them on similar numbered lines, measuring in each instance from the line £'F'. 
Tracing a line through these points will give the half pattern shape E^PF^. No matter 
what shape the dormer may have, or whether the main roof is inclined or curved, the 
principles are the same. 

FIG. 67. Shows a dormer in which the curves in elevation are struck from the centers 
a, b and c and the roof having the incline //;. The main roof is curved, the arc de being 
struck by a given radius. Find the tnie profile, also the pattern for one-half of dor- 
mer roof and half the opening for the main roof. 



44 



THE NEW YORK TRADE SCHOOL'S 



PATTERNS FOR MITERS BETWEEN MOULDINGS OF DIFFERENT PROFILES 

FIGS. 68, 69. When different shaped mouldings are to join together at various 
angles, either inside or outside miters being desired, the principles illustrated in Fig. 68 
should be employed. A and B represent two dift'erent mouldings to be joined together 




Fig. 67. 



at a right angle. Divide either one of the profiles (in this case .4) into an equal number 
of spaces as shown by the small figures i to 9, from which points horizontal lines are 
drawn, intersecting the profile B from i' to 9'. To obtain the pattern for the mould A 
mitering against the mould B, take the stretchout of A and place it on the \'ertical line 
BC as shown. Draw the usual measuring lines to intersect vertical lines drawn from 
similar intersections in B. Trace the pattern line FG. In similar manner obtain the 
pattern for the mould B, mitering against the mould A. Take the stretchout of B 
(measuring each space separately because they are all unequal) and place the spaces on 
the vertical line DE, as shown by similar numbers. From these points horizontal 
lines are drawn, which are intersected by vertical lines dropped from the profile A. Trace 
the pattern line JK. If the patterns shown by the solid lines were formed up according 
to their respective profiles and then joined together they would form an interior angle 
shown by HEJABC in Fig. 69. If an exterior angle were desired as shown by NBLFED 
it would only be necessary to take the opposite pattern cuts shown dotted by H and L 
in Fig. 68, which would give the desired angle. 

FIG. 70. In Fig. 70 is shown the front and side view of a keystone, to which the 
principles explained in Fig. 68 are applied. The patterns are to be developed for A and B. 

FIG. 71. Shows the intersection between a vertical and inclined moulding in eleva- 
tion. In this case, before the patterns can be developed, the miter line between the 
two moulds in elevation must first be obtained and the method is easily traced by re- 



TEXT BOOK ON PATTERN DRAFTING 45 

ferring to the plan and elevation, the angle i-a being 45°. The profiles in plan and 
elevation are similar. The pattern for A and the opening to be cut in the mould B are 
both to be developed. 




Fic. 69. 



(E 5 X)' 




Fig. 70. 



FIG. 72. When an inclined moulding, as B in Fig. 72, is to be mitered to the return 
of the horizontal mould A, at an angle shown by A^ in plan, then divide either one of 
the profiles (in this case cd) into an equal number of spaces, and from these points, 
parallel to ca, Hnes are drawn intersecting ab. To obtain pattern for the incHned mould- 
ing B, the stretchout of a-b is laid out on a'-b' and the intersections in the pattern ob- 
tained from cd. For the pattern of the return, shown by A' in plan, the stretchout of 
cd is placed as shown by c'd' and the intersections in the pattern obtained from the 
projection of the mould ab as shown. A'- is then the pattern for the return of A, and 
Z?' the pattern for the inclined mould B. 

FIG. 73. When two unequal moulds are to be joined horizontally at other than 
a right angle in plan, the method shown in Fig. 73 is employed. In this case A and 
B are the two profiles, one of which (.4) must be divided into convenient spaces, shown 
from I to 10, then horizontal lines drawn, intersecting B from i' to 10'. Draw the 



46 



THE NEW YORK TRADE SCHOOL'S 



proper angle, whether interior or exterior, as shown by CDE in plan, and place dupli- 
cates of the profiles in their proper positions as shown. Parallel lines are drawn in plan 
intersecting each other from i° to io°. The patterns for .4' and B^ are developed in 
the usual manner, the stretchout taken from each mould being indicated by similar 
figures. 





PATTERNS FOR VARIOUS BUTT MITERS 

FIG. 74. Illustrates the principle applicable to various butt miters, whether the 
moulding or other object butts against a plain or curved surface in either plan or eleva- 
tion. Let A represent the profile of the mould in elevation butting against the plain 
surface BC or curved surface DE, the curved surface being struck by a radius equal to 
li inches. Divide the profile into equal spaces and draw lines parallel to the fines of 
the moulding until they intersect BC and DE. The stretchout of A is then laid out 
on GF, the usual measuring lines drawn, which are intersected by vertical lines drawn 
from the various intersections on BC and DE. The miter cut 5'C' is the pattern for 
the mould .4 butting against the plain surface BC in elevation. It will be noticed that 
where the vertical surfaces 1-2 and 6-7 in the profile A, butt against the curved line 
ED, similar surfaces in the pattern will be reproductions of these curves. To obtain 
these curves in the pattern take the radius of the curve DE, and with i'-2' and 6'-7' 
in the pattern as centers, draw arcs intersecting each other at a and h respectively. 
Using the same radius, with a and b as centers, draw the arcs i'-2' and 6'-7'. Then 



TEXT BOOK ON PATTERN DRAFTING 



47 



E^D^ is the butt miter against ED in elevation. The above principle is applicable for 
returns against plain or curved roofs, domes or drops on the faces of brackets. 



OBTAINING DIVISIONS 




pattern for b' 

Fig. 73. 




'^ELEVATION 
C D 



Fig. 74- 



48 THE NEW YORK TRADE SCHOOL'S 

FIG. 75. In Fig. 75, A shows the profile of a moulding butting against the plain 
surface BC and curved surface DE, in plan. Obtain the pattern showing the two cuts. 

FIG. 76. Shows the front and side view of a bracket. The drop A is to butt against 
the curve B, as shown in side view. The stretchout should be laid ofT as indicated by 
a-b and the full pattern developed. 

FIG. 77. Shows another style of bracket, the pattern for the return around a, b, c 
to be laid out in one piece. 



(E4X) 




A 








K^- 


a 


B L^ 






(E4X) 


I 







Fig. 75- 



front side 

Fig. 76. 



(E4X) 




Fig. 77- 



FIG. 78. Shows an inclined moulding .4 in elevation, butting against an oblique 
surface a-b in plan. In cases of this kind the miter line ef in elevation must first be 
obtained. This is done by taking a duplicate of the profile in A and placing it as shown 
by A' in plan. Lines are projected against the plain surface (or curved surface which- 
ever it may be) a-b, from which vertical lines are erected and intersected by similar 
numbered lines, drawn from the profile in A, parallel to the lines of the moulding. The 
stretchout is then laid oR on cd drawn at right angle to A. 




ELEVATION 



Fig. 78. 




Fig. 79, 



FIG. 79. Shows another case of a horizontal moulding butting against a plain sur- 



TEXT BOOK ON PATTERN DRAFTING 



49 



face ab in elevation, the moulding being placed in an oblique position when viewed in 
plan. The same operations are gone through as in Fig. 78, the difference being that 
the position of the mouldings are reversed in Fig. 79. A' is a duplicate of A, and after 
the miter line BC in plan has been obtained, the stretchout is laid off at a right angle 
to the lines of the moulding in plan as shown by de. 

FIG. 80. When a moulding is to butt against a dome or sphere, the work is done 
as shown in Fig. 80, where the center line AB must first be drawn, and with F as center 
draw the one-quarter plan of the dome DB. Above this in its proper position, using E 
as center, draw the half elevation of the dome shown by ACF. Place the profiles G 
and G"' in their proper positions in both elevation and plan respectively, and divide each 




Fig. 80. 



into the same number of spaces. From the divisions in C draw horizontal lines until 
they cut the curve DB, from which points, erect vertical lines cutting the base line CE 
of the dome as shown. Now, using E as center, with the divisions on the base line as 
radii, draw arcs, which intersect by lines drawn from similar numbers in the profile 6", 
parallel to the lines of the mouldings, giving the miter cut HJ. The stretchout is laid 
off on the vertical line ab. When developing the pattern, the arcs HK and LJ are 
obtained by using as radii the distances c and d respectively. As that portion of the 
profile G from / to n cuts the dome on a horizontal plane, the radius with which to 
strike the arc from L to A' on the pattern is obtained by using the distance through LA', 
shown from e to /; for it is evident that all horizontal planes are true circles and there- 
fore the plane through LA' has a radius equal to cf. 



5° 



THE NEW YORK TRADE SCHOOL'S 



PATTERN FOR DROP ON A SPHERE 

FIG. 8i. In making up urns or vases, it is usual to place drops around the sphere 
or other object to give an ornamental finish. The principle employed in developing 
the face and return strip is shown in Fig. 8i. First draw the center line ^4^^ and using 
B in elevation as center, draw the semi-sphere CDE. Below the elevation draw a hori- 
zontal line as FG, crossing the center line at H. In this case the sphere is to be encircled 
by a band having four drops. Therefore, from the center H draw the radial lines HI 
and HJ at 45°. Add the projection of the band in elevation shown from E to T, and 
with BT as radius and H in plan as center, draw the semi-circle G^^'F, cutting the radial 



ELEVATION 




pattern for return 
stripX 



Fig. 81. 



lines as shown, and from these intersections extend vertical lines into the elevation as 
P and J\ which lines represent the seam lines. Within the points /' and y draw the 
elevation of the drop as shown, struck from the center V. Divide the quarter circle 
shown from i to 4, from which points horizontal lines are drawn cutting the sphere ED 
from i' to 4'. These horizontal hues then represent planes, the sections of which are 
true circles and are obtained by projecting vertical lines from points i' to 4', cutting 
the center line FG in plan from i" to 4". Witli H as center and the various points i" 
to 4" as radii, draw semi-circles as shown, which are intersected by vertical lines dropped 



TEXT BOOK ON PATTERN DRAFTING 



SI 



from similar numbered points in the elevation V, resulting in the points of intersections 
in plan i° to 4°. Extend these lines until they cut the semi-circle GF from i" to 4". 
Then a-i°-4°-4''-i''-6 represents the half soffit plan of one drop and is all that is required 
for developing the pattern. Notice that all of one-half of soffit plan has been drawn. 
This is done in order to show how the complete elevation would appear, when the var- 
ious intersections in plan have been projected to the elevation. If six or eight or any 
number of drops were to encircle the sphere, it would only be necessary to divide the 
plan into the desired number of spaces and obtain the points as shown in this case by 
/' and J\ inside of which the elevation of the drop is drawn. To get pattern for the 
return strip X in elevation, double the distance i to 4 in elevation, and place it on the 
horizontal line GS, at right angle to which vertical lines are drawn and intersected by 
horizontal lines drawn from the intersections 4° to 1° and i"" to 4''. Draw a line 
through points thus obtained, and extend on each side by tracing the bottom of the 
horizontal band shown in plan by a-fc-i^-i°, resulting in a-b. Then will a-b-K-L- 
M-b-a-N be the desired pattern. The pattern for the face is obtained by taking twice 
the stretchout of the spaces contained in 64'^ in plan, and placing them on the line TU. 
Vertical lines are drawn and intersected by horizontal lines drawn from similar num- 
bers in elevation. bOPRb is then the pattern for the face, four such pieces being re- 
quired to encircle the sphere. 

FIG. 82. In this figure a-b-c represents a spun ornament. The plan is a true circle, 
one half being shown by def. Four drops shown by .4 will encircle the ornament, the 




HALF PLAN 



Fig. 82 



location of the seams being shown by 5-5. Develop the pattern for the face A and 
its return strip, using the principles given in Fig. 81. 



52 



THE NEW YORK TRADE SCHOOL'S 



PATTERN FOR INCLINED MOULDING ON A WASH 

FIG. 83. The principles used in developing this problem are similar to those given 
in connection with Figs. 78 and 79, the only difference being in the position of the 
moulding in Fig. 83. ABC represents the half elevation and CD the section showing 
the pitch of the wash. Place the sections or profiles of the mould in their proper posi- 
tions in both views, as shown by E and E\ and divide each into the same number of 
spaces. From the divisions in the profile E drop lines until they intersect the wash as 




(E4X) 




PATTERN FOR Y/ASH 



Fig. 83 



shown, from which points horizontal lines are drawn in the elevation and intersected 
by lines drawn parallel to the lines of the inclined moulding, from similar intersections 
in the profile E\ If a line is traced through points thus obtained, it will show the miter 
line i' to 8'. The miter line being obtained, the pattern for the inclined moulding is 
developed by laying off the stretchout of E or £' on EG and intersections obtained in 
the usual manner as shown. If the triangular piece a-b-8' was to be added to the 
pattern, then with &'-b and a-b in the elevation as radii, and 8' and a in the pattern as 
centers, describe arcs intersecting each other at b. Draw lines from a to 6 to 8' as shown. 
To obtain the cut in the wash so as to admit of the mitering of the inclined moulding, 
take all the divisions contained on the wash in the section and place them on the ver- 



TEXT BOOK ON PATTERN DRAFTING 5,1 

tical line H't as shown. Draw the usual measuring lines, which intersect by lines dropped 
from similar intersections in the miter line i' to 8'. Then LM is the desired cut. 

Applying the method just explained, develop the inclined moulding and wash when 
the inclined moulding has similar dimensions as shown in Fig. 83, but the wash is 
curved, as shown from A' to Y, the profile E- being similar to E. An additional point 
a' must be used, intersecting the curve at a". Why this has been done will become 
evident when developing the patterns. 



PATTERNS FOR RAKED MOULDINGS 

FIG. 84. When an inclined moulding is to miter with a horizontal return, whether 
the plan is a right angle or any given angle, a change in the profile in one or the other 
of the mouldings is necessary before the patterns can be developed. Hence the term 
raked moulding. This means a moulding the profile of which is a modification of the 
normal or given profile. In Fig. 84 let ABC represent the elevation of a pediment, 
mitering with a horizontal return moulding at top and bottom, at a right angle in plan, 
as shown by EJF. In drawing the elevation, establish the point 7' and draw the hori- 
zontal line 7'-C and the inclined line y'-y". As the incHned moulding is to have the 
normal or given profile, place this profile D in its proper position as shown. Take a 
duplicate of D and place it in its proper position in plan as shown by D' and complete 
the plan FJEHG. 

Divide both D and D' into the same number of spaces, and through D parallel to 
j'-j" draw Hues indefinitely. Through D' in plan and parallel to FJ, draw Hnes inter- 
secting the miter line JG, from which intersections erect vertical lines, intersecting the 
lines previously drawn parallel to j'-j". The result is the miter line and profile B. 
Parallel to the lines of the inclined moulding, draw a-b, perpendicular to which draw 
lines from the intersections in the profile D, cutting a-b from i to 9. Establish the 
point i" in elevation, and take the various distances on a-b and place them on the hori- 
zontal line a"-b", being careful to have the point i come directly over i". From the 
various intersections on a"-b" drop vertical hnes, intersecting similar lines in the inclined 
moulding, giving the miter line or profile .4. When the horizontal moulding returns 
at a right angle in plan as in this case, the plan is not necessary in obtaining the pro- 
file B, but is shown here, to give the principles necessary in obtaining the miter line in 
elevation when the plan is other than a right angle. The profile or miter line B could 
be obtained by taking the various divisions on a-b, and placing them as shown by 
a'-b', and intersecting lines as in A. The raked profiles A and B having been obtained, 
the patterns for the inclined moulding and top and bottom returns are ready to be 
developed. The pattern for B need not be developed from the plan when the return 



54 THE NEW YORK TRADE SCHOOL'S 

is a right angle, but is here shown, to explain the principles which must be used when 
the plan has an angle other than a right angle. The stretchout of B is placed on KH, 
the usual measuring lines drawn, and intersected by lines extended from the miter line 
JG; I'-o being equal to HG. 5' is the pattern for the return B. This rule is appli- 
cable for any angle. To obtain the patterns for the right angle returns B and A, with- 
out using the plan, apply the method for cutting a square miter. Take the stretchouts 
of B and A and place them as shown respectively by LM and PR, bearing in mind, 
that while the normal profile D is divided into equal spaces, the raked profiles B and A 
have unequal spaces, and each one of these spaces must be carried separately onto their 
respective stretchout lines. Draw the usual measuring lines, which intersect by vertical 
lines, dropped from similar points in the profiles B and A. Make the distance NL and 
PS each equal to HG in plan, or the desired depth of the return. Then 5" and A' 
represent the patterns for bottom and top returns. The pattern for the inclined mould- 
ing is obtained by placing the stretchout of D on the line TU, which is drawn at right 
angle to the inclined moulding. Measuring lines are drawn and intersected by lines 
drawn parallel to TU from similar intersections in B and ^4. The desired pattern is shown 
by VWXY or D\ 

FIGS. 85, 86 and 87. Raked mouldings are frequently met with in cornice work 
and in order that the student shall have ample practice in developing this class of pat- 
terns, a number of such problems are given. The first problem to be drawn is a pediment 
having an outline similar to hijk in Fig. 84, but the return of which has an angle shown 
by cde in plan. The miter line dj is obtained as shown. The normal profile is to be 
placed in the inclined moulding as shown by D, and the upper return is to return at right 
angle in plan. It will not be necessary to develop the upper return as this was done 
in the preceeding problem, and therefore the elevation can be broken on the line ZZ. 
As the given profile is in the inclined moulding, a duplicate of same must be placed 
on the line dc in plan, and the miter line projected in the elevation in exactly the same 
way as in the right angle return. The patterns for the lower part of the inclined 
moulding and the horizontal return cd in plan are to be developed. The second problem 
is to use the same elevation as before, but place the normal or given profile at the foot 
of the gable as at D in Fig. 85, and obtain the raked profiles of the inclined and upper 
mouldings, also the patterns for the lower, inclined and upper mouldings when the 
plan is a right angle, in which case no plan is necessary as previously explained. The 
third problem is to have the same elevation as in Fig. 84, with the normal profile in 
the horizontal return as shown at D° in Fig. 84, but this return to have an angle as 
shown by cde in plan. As the horizontal return has the normal or given profile, a 
duplicate of D° must be placed on the horizontal return cd in plan and the miter line 
in elevation projected as before. In this problem the patterns for the upper return, 
and the inclined and lower return mouldings are to be developed, after the raked 
profiles of the inclined moulding and upper return are obtained. The fourth problem 



TEXT BOOK ON PATTERN DRAFTING 



55 




Fig. 84. 



56 



THE NEW YORK TRADE SCHOOL'S 



is given in Fig. 86, which shows a curved moulding, joining a horizontal moulding at 
right angle hij in plan, D being the normal profile. The same principles are employed 




Fig. 85- 



as in Fig. 84, with the exception that concentric curves are drawn in elevation, using 
e as center in Fig. 86. The raked profile Z)' for the curved moulding is obtained by 
drawing lines at right angles to cd and these lines are intersected from divisions on 
a'b', which are obtained from the line a-6. Obtain the pattern for the right angle 
return hi in plan, without using the plan view. The method of developing the pattern 
for the curved moulding will be explained in Part Two. The fifth problem is to develop 
the pattern for the horizontal return joining a curved moulding at an angle shown by 




PLANS 

VI\\\m\\\m\\\\m\ \\\m\M\\\m\mm\\\\\\,A,.\\\\m^^^^^ 



n 



Fig. 86. 



TEXT BOOK ON PATTERN DRAFTING 57 

mno. In this case the plan must be used, and as the normal profile is given in the 
horizontal return, a duplicate of D must he placed on line with m-n in plan and ele- 
vation and the miter line obtained in elevation. From these intersections concentric 
curves are drawn and the raked profile D' obtained as before. The sixth problem is 
to obtain the raked profile and pattern for a horizontal return when the normal profile 
is given in the curved moulding as at D- and the plan is a right angle. In this case 
the profile D' must be divided into equal spaces, from which points perpendicular lines 
are drawn to the center line. Then using e as center, concentric curves are drawn, 
and in turn, intersected by lines erected from a-b on which the projections of the 
various spaces in D^ are placed. Should the circle be of such size that the center line 
ce could not be used, then any radial line as se can be taken, on which to project the 
divisions in D^, bearing in mind that the profile D' must always be placed at right 
angle to the radial line. The seventh problem is to obtain the raked profile and pat- 
tern for the horizontal return when the normal profile is in the curved moulding and 
the angle is an octagon as shown by ni-n-o. As the given profile is in the curved 
moulding, a duplicate of D- must be placed in line with ii-o in plan, and the miter line 
projected to the elevation, as previously explained. From the intersections obtained 
in elevation, horizontal lines are drawn and intersected from projections obtained from 
the profile D-, giving the raked profile from which the stretchout is obtained and used 
to develop the pattern for the return at right angles to m-ii in plan. The eighth prob- 
lem is given in Fig. 87, and shows the principles used when any number of gables are 
to be joined together at any angle in plan. Part of the front elevation of a gable is 
shown, four of which are to be joined at right angles in plan. A is the given profile 
and is duplicated at ^4' in plan, the miter line cd in elevation being obtained as shown. 
In both, Figs. 84 and 87, the plan is not required as the gables join at a right angle, 
but is now shown to explain the principles which apply when the angle is other than 
a right angle. Without using the right angle plan, all that is necessary, is to obtain 
the projection from A on the line ab and place the divisions as shown by a'b' and 
obtain cd. Solve this problem without using a plan and develop the pattern for the 
gable moulding ic, and add to the pattern the roof of the gable, by placing the dis- 
tance of the ridge line tit at right angle to the line of the pattern ic and draw a line 
from h to c in the pattern. The ninth problem is to draw an elevation similar to that 
shown by the front elevation in Fig. 87, eight gables of which are to join at octagon 
angles in plan as shown. When drawing this problem, complete a quarter plan of the 
eight gables through ih in elevation, similar to that shown in the reduced diagram J, 
showing the ridge and valley lines. A being the given profile, place a tracing of same 
in the octagon plan at A^ and proceed to obtain the miter line in elevation. Develop 
the pattern for the gable mould ; the plan of which is an octagon, and add the roof to 
same by placing the length of the ridge line m-n in diagram J, at a right angle to the 
line of the pattern — corresponding to ic, and drawing a line or valley line h to c in the 



58 



THE NEW YORK TRADE SCHOOL'S 



pattern. The tenth problem explains the principles to use when gables are to be 
joined and when the sides are of unequal widths. In this problem four gables are to 
be joined, the front and side of which are equal to that shown in Fig. 87, the given 
profile being shown at A and the modified or raked profile at B in side elevation. Should 
the given profile be placed in the side elevation, the raked profile in the front would 




Fic. 87. 



be obtained in precisely the same manner as that which will follow. The miter line 
cd being obtained as before, a horizontal line is drawn from d, meeting the \-ertical 
line in side elevation at d'. A duplicate of cd is placed in position as shown by c'd'. 
The center line in the side elevation is now established and a line drawn from i in front 
view, intersecting this center line at /. Draw a line from / to c'. Draw lines parallel 
to df as shown and place the divisions of ab on a"b" and obtain the raked profile B. 
As the pitch in the front elevation is less than that of the side, it will be found when 
drawing this problem to enlarged size, that a double line will show as at d" in diagram 



TEXT BOOK ON PATTERN DRAFTING 



59 



F, while a single line shows in side elevation, owing to the small size of the drawing. 
Why this double line appears will become evident when solving the problem. Obtain 
the pattern of the front gable by taking the stretchout of .4 and placing it at right 
angle to ic, and add the roof to this pattern by taking the distance of the ridge line 
ef in side, and placing it at a right angle to the line in the pattern, corresponding to 
ic in front. For the pattern of the side gable, use the stretchout of the raked profile 
B, and when adding the roof to the pattern take the distance of the ridge line lii in 
front. The eleventh problem is to obtain the patterns for eight gables, joining at 
octagon angles in plan, each alternate side being different in width, similar to that 
shown in diagram M. Let the front elevation in Fig. 87 represent one of the wide sides, 
and the side elevation, one-half of one of the narrow sides, the given or normal profile 
to be placed in the wide side, as at A. Draw a quarter plan of the gables below the 
front elevation, through ih in elevation, showing the ridge and valley lines in plan, from 
which the true lengths of the ridge lines can be obtained, as shown reduced in diagram 
M, in which rs shows the ridge line for the wide side, and rt the length for the narrow 
side. Place a duplicate of the normal profile .4 in the quarter plan just drawn, in the 
position shown by A- in plan, and obtain the miter fine ai in elevation in the same 
manner as in the square gable. Transfer cd to the side view and obtain the raked 
profile B. What has been said about the double line in F is also applicable to this problem. 
When laying out the pattern for the wide side, use the stretchout of A and add 
the roof pattern by placing the length of the ridge for the wide side rs in M, as ex- 
plained in connection with the square gable. For the pattern of the narrow side, use 
the stretchout of B, and for the roof pattern add the length of the ridge rt in M. Should 
the normal profile be placed in side view, the raked profile in front would be obtained 
by reversing the operations. 



PATTERN FOR GUSSET PIECE 

FIG. 88. When two pipes of unequal diameters intersect each other, and a gusset 
piece is required to strengthen the joint or intersection, the principles to be employed 
(whether the smaller pipe joins the larger at right angles or not) are shown in Fig. 88. 
.4 is the end view of the large pipe, and B the side view, C and C representing the 
sections of the smaller pipe. Establish at the desired distances the height and pro- 
jection 7' and 7" of the gusset piece, and draw a line from 7' to 7". Divide the circles 
C and C into equal spaces as shown, being careful to place the vertical line 1-7 in C 
in a horizontal position in C. Drop vertical lines from C to A, from which points hori- 
zontal lines are drawn and intersected by vertical lines, dropped from similar num- 
bered intersections in C from i to 4, and resulting in the miter Hne 6-4'. From 4' 
draw a line to 7', and from the intersections 4 to 7 in C\ drop vertical fines cutting 



6o 



THE NEW YORK TRADE SCHOOL'S 



the miter line 4'-;' as shown. From the various intersections on 4'-?', draw Hnes 
parallel to y'-y" indefinitely, intersecting similar horizontal lines previously drawn from 
A and resulting in the points of intersections 5" and 6". f-y is then the Hne of joint 
between the gusset piece and small pipe, and 4'-^" the joint line between the gusset and 
large pipe. A true profile must now be obtained of the gusset piece, at right angle to 
7'-7" or through the line n-4', and is obtained by taking a tracing of 4-7-4 in C and 
placing it in the position shown by C'. Perpendicular lines are drawn, as shown, inter- 
secting similar lines previously drawn. Then 4°-7°-4° is the true profile through a-4'. 




Fig. 



Take a stretchout of this profile and place it on the line DE drawn at right angles to 
7'-7". Draw the usual measuring lines, which intersect by lines drawn at a right angle 
to 7'-7" from similar numbered intersections on 7'-4' and 4'-7". It will be noted that 
the half pattern is shown, the full pattern being required and is obtained by reversing 
on the line 7''7^. Obtain the true profile and pattern for a gusset piece, to be placed 
between the pipes forming an acute angle, when the profile of the small pipe is to be an 
ellipse as shown in end view Fig. 88, and the angle of the small pipe to be similar to the 
dotted line db in front view. In this case the minor axis of the ellipse ef must be placed 
at a right angle to the line of the pipe bd in front view, the ellipse to be drawn by the 
method given in Fig. 8. 



TEXT BOOK ON PATTERN DRAFTING 6i 



PATTERN FOR PANELED LEADER OFFSET 

FIG. 89. Occasionally a leader or conductor passes down the interior angle of a 
wall and makes an offset over a wash or other object as shown in Fig. 89. CD represents 
the wash over which the leader is to pass, but at an angle shown by AB in plan. In 
this case it is desired that the miter lines appear in the elevation as shown by le and 

ik, the Hnes through i and e and i and k to show horizontal lines when viewed from 
the front. Draw the plan of the wash CD, as shown by AB, and place the sections of 
the leader in position as shown by A and B and connect similar corners as shown. 
Project the elevation of the pipe and draw the section of the panel heads as shown by 
cdcfh and ijkiuii. Having drawn the plan and elevation, the pattern for the vertical 
pipe C is obtained by taking a tracing of that part and placing it as shown by C°, at 
right angle to which the stretchout line c'd' is drawn. On this line the stretchout of 
either A or i? in plan is placed and the pattern obtained in the usual manner. The 
opposite of the pattern for C° will answer for the pattern for the lower pipe D. To 
obtain the pattern for the middle section of the elbow, an oblique view must be drawn 
as follows: Parallel to i-i in plan and of equal length draw the line I'b'. From i in 
elevation draw the horizontal line i-b, cutting the line projected from ^. Take the 
height b J and place it on the line i-b' extended in the oblique view, as shown from b' 
to 1°. Draw a line from 1° to i', which is the true length of the pipe on i-i in plan. 
From the various intersections i to 8 in the section A at right angle to i-i draw lines 
indefinitely, as shown. Measuring from the line bi in elevation, take the various dis- 
tances to points I to 8 on the miter line i e, and place them on similar numbered lines 

n the oblique view, measuring in each instance from the line b'l', and resulting in the 
miter line 1° to 8°. Parallel to i°-i' from these intersections draw lines as shown. The 
next step is to obtain the true profile of this oblique view by extending the lines just 
drawn, at a right angle to which draw the line LM. From any point as a in plan, draw 
the perpendicular aR, crossing the lines shown. As a is placed upon the line 8-8 in 
plan, then the intersection of the line LM with the line drawn from 8° in the oblique 
view as shown by 8', will represent similar point. Now take the various distances from 
a in plan to lines 7-6-5-4-3-2 and i and place them in the oblique view, on similar num- 
bered lines measuring from the line LM. Then E is the true profile for the middle section 
of the pipe. The stretchout of E is now placed on a Hne drawn at a right angle to j°F 
and the pattern obtained as shown. G then represents the pattern for the upper part 
of the middle section of the elbow, and H the pattern for the lower miter. The patterns 
for the panel heads are obtained as follows: Wliere the points cdefh, and ijknin in eleva- 
tion touch the various bends, project same into the plan intersecting similar numbered 



62 



THE NEW YORK TRADE SCHOOL'S 



bends, as shown by the small dots. Now take the stretchouts of cdefh and ijkmn and 
place them at right angles to A and B, respectively in plan, as shown by similar letters. 
Draw the usual measuring lines, which are intersected by lines drawn from similar points 
of intersections shown by the dotted lines. Then will TV be the pattern for the panel 
head shown by ceh in elevation, and O the pattern for the head shown by i-k-n in eleva- 
tion. If it were not necessary for the lines through J and e in elevation to be horizontal 




Fig. 89. 



lines, when viewed from the front, the patterns for this elbow could be developed by 
using the same profile ^4 or B throughout the entire elbow without any change of profile, 
but the miter line would pass through the diagonal line of the pipe. Further practice 
in this principle is given in the next problem. 

Develop the patterns for an elbow similar to that shown in Fig. 89, using the profiles 
A or B throughout the entire pipe. In this case it is only necessary to construct the 



TEXT BOOK ON PATTERN DRAFTING 63 

oblique view i°-i'-b' as before, then bisect the angle 5i°i' by means of the arc rs and 
intersecting arcs t and draw the miter Hne t-i°-w. The intersections i to 8 in A are 
then projected until they cut the miter line tw as shown. The stretchout of .4 is now 
placed at right angle to i°5, as shown by a'b', and the pattern obtained the same as in 
ordinary elbow work. This one pattern then answers for all of the cuts for the entire 
elbow. While this is a simple nile it can only be used when the miter line runs through 
the diagonal of the pipe. 



64 THE NEW YORK TRADE SCHOOL'S 



PATTERNS FOR A RAKING BRACKET 

FIG. 90. Shows the method of developing the face and side of a raking bracket. 
The normal side is shown by C, and the normal face of the drop is shown by D. First 
draw the rake which the moulding is to have, as shown by AB. Place in its proper 
position the side of the normal bracket C drawn at a right angle to the rake ; draw the 
face of the drop D and also the side of the cap J. In enlarging this drawing, more spaces 
should be employed then here shown. Establish at pleasure the point E and draw the 
vertical line EF. Divide the normal face D, also the circle in same, into equal spaces, 
and draw lines parallel to the rake as shown. Now take a tracing of D and place it as 
shown by D\ so that the side Z will be in line with E-F. From the various points in 
Z)' erect vertical lines intersecting similar lines drawn from D. A line traced through 
points thus obtained, as shown by 6^, i, 2, 3, 4, 5, 6, 7 and F will be the raked face 
of drop. Extend G-i to H. For the pattern of the return strip of drop D^, take the 
stretchout of 1-7 in D'' and place it on the line 6~V extended in the normal bracket as 
shown by a-b. Draw the usual measuring lines which intersect by lines drawn at right 
angle to the rake from similar intersections on the curve 8-13, resulting in the pattern 
shown. For the pattern of the lower face of the bracket, divide the normal side into 
equal parts shown from 8 to 13, from which points lines are drawn parallel to the rake, 
intersecting the sides of the raking bracket GH and EF as shown. At a right angle to 
HE draw the stretchout line cd, upon which place the stretchout of 8-13 in the normal 
bracket. Draw lines at right angle to ai, which intersect by lines drawn from similar 
intersections on GH and FE at right angles to HE, resulting in the pattern shown. From 
these same intersections on one of the sides of the raking bracket as FE and at right angle 
to it, draw horizontal lines as shown, crossing the vertical line m'n' previously drawn. 
Now measuring in each instance from the line viii in the normal side, take the various 
distances to points 6, r, 8 to 13 and place them on similar lines, measuring in each 
case from the line m'n'. A line traced through these intersections will be the pattern 
for the side of the raking bracket. Divide the normal profile of the cap J into equal 
spaces shown from i to 6, from which points draw lines parallel to the rake indefinitely. 
Take a tracing of J and place it on either side of the raking bracket as shown by J\ 
From the various intersections in J\ erect lines intersecting similar lines drawn from J. 
K then represents the profile of the upper return and L the profile of the lower return. 
To get the pattern for the cap face of the raking bracket, take the stretchout of J in the 
normal side and place it at right angle to the rake as shown by ef, the measuring lines 
being intersected by lines drawn from similar points in L and K. For the patterns of 
the returns K and L, take the stretchout of each and place them on the line mn extended, 
as shown respectively by ih and hj. Draw the usual measuring lines which are inter- 
sected by lines drawn parallel to mil. from similar numbers in the profiles J and J, 



TEXT BOOK ON PATTERN DRAFTING 



65 



resulting in the patterns for the returns K and L. Using the same principles given in 
Fig. 90, develop the patterns for the drop, face and side, when the normal face and side 
is to be as shown by V and X. In this case, the only points necessary to develop the raked 
face of drop T are shown by the small dots. The patterns for the cap need not be laid out. 



PATTERN FOR 




Fig. 90 



PATTERNS FOR A RAKING OCTAGONAL BALUSTER CAP 

FIG. 91. Shows the method of obtaining the various patterns for a raking octagonal 
l)aluster cap. The same principles can be used, no matter how many corners the plan 
may have or whether the plan has interior or exterior angles ; it also being immaterial 
what pitch the mould may have in elevation. Let ABCDEF represent the half plan. 
Place the normal profile on CD as shown by H, which divide into equal spaces as shown 



66 



THE NEW YORK TRADE SCHOOL'S 



and complete the plan a-b-c-d. Draw the miter lines Ea, Db, Cc and Bd. Draw the 
elevation of the body of the baluster as shown by LIJK. Take a tracing of H in plan 
and place it as shown by //' in elevation which represents the given and true profile for 
the middle part of the baluster. Through the various intersections in //' draw lines 
parallel to LK, which intersect by vertical lines erected from similar intersections on the 
miter lines Ea, Db, Cc and Bd and resulting respectively in the miter lines M, N, and 



TRUE ANGLES 

ON L-K 




PATTERN 
FOR 



PATTERN FOR 



Fig. 91. 



P in elevation. The intersections have not been numl:)ered, but by following the dotted 
lines, the points of intersection are made clear. The various sides of the mould have 
been marked in plan 1° to 5°. For the pattern 3°, take the stretchout of //' in elevation 
and place it as shown by kj. Draw the usual measuring lines, which intersect by lines 
drawn at a right angle to LK from similar intersections in the miter Hues N and 0. To 
get the patterns for 1° and 5° in plan, take the stretchouts of PL and KM and place them 
as shown respectively by cf and hi in plan, and obtain the patterns from intersections 
on the miter lines Bd and Ea as shown. 

Before the patterns for 2° and 4° can be developed, true elevations and profiles must 
be obtained. Take a tracing of 2° and place it in the horizontal position shown by 2°°. 



TEXT BOOK ON PATTERN DRAFTING 67 

From the various intersections on Cc in 2°°, erect vertical lines, which are intersected 
by horizontal lines drawn from similar points in the miter line On in elevation, resulting 
in the miter line RC in the true elevation. From L in elevation, draw the horizontal line, 
which intersect by the vertical line erected from B in 2°°. Draw the line TC which 
represents the true pitch. Parallel to TC from the various intersections in CR, draw^ 
lines indefinitely which are intersected by vertical lines, erected from Bd in 2°°, and 
resulting in the miter line ST. STCR is then the true elevation of the side 2° in plan. 
A true profile must now be obtained by placing a tracing of the normal profile H in plan, 
as shown by //% and drawing perpendiculars, resulting in the true profile H^. Take a 
stretchout of W and place it as shown on rs and obtain the pattern for 2° as shown by 
the dotted lines. In precisely the same manner obtain the true elevation and profile 
for 4° in plan, as shown respectively by WXVU and //^ The stretchout of //' is placed 
on til and the pattern obtained as shown. It should be understood that when the position 
of all the members as P, 0, N and M are vertical the pattern for each side must be ob- 
tained as explained. When, however, a given profile can be used throughout the entire 
pitch, so that the members will stand at right angles to the rake, the method to be em- 
ployed is as follows : At a right angle to LK from L, 11, m and K draw lines indefinitely as 
shown. Parallel to LK draw L^K\ Measuring from the line AF in plan, take the various 
distances to B, C, D and E, and place them on similar lines, measuring from the line 
UK^ and obtain 5', C, Z>' and £\ which will represent the true half section and angles on 
LK. Assuming that the profile H in plan is to be used, it is only necessary to place same 
as shown by //" after the miter lines x-w and v-C- have been obtained. The patterns 
are then developed in the usual manner. 

FIG. 92. Applying the principles explained in preceeding problem, develop the 
patterns for an eave and gable moulding, having a pitch equal to F5 in elevation in Fig. 
92 and a plan, as shown by ABODE. The eave mould H in this case is to be so placed 
that 1-2 and 3-4 are in vertical positions. From the corners i to 5 in // lines are drawn 
parallel to F5 as shown. Take a tracing of H and place it as shown by //' in plan and 
obtain the miter lines Bj, Cf and D^. Lines are erected from miter lines to intersect 
similar lines in elevation, as shown by the miter lines J and /. To obtain pattern for 
the eave mould H, take the stretchout of H and place it on a-b in plan, and obtain pattern 
from intersections on the miter line D^. Take a tracing of H and place it as shown by 
H^ and obtain the true profile for the mouldings HI and JK, as shown by //^ The 
stretchout of W is now placed on cd and ef, and the patterns for the mouldings HI and 
JK are developed from intersections in H and /, and J and K respectively. Before 
the pattern for IJ can be laid out, a true elevation and profile must be obtained as follows : 
Take a tracing of BC in plan and place it as shown b}^ B'^C^. From C lines are erected 
and intersected by those drawn from / in elevation, resulting in L. From 5 in 5' erect a 
line which intersect by a line drawn from 5° in J. Draw a line from 5 to 5 in the true 
elevation, and parallel to same from the points in L, draw lines which are intersected 



68 



THE NEW YORK TRADE SCHOOL'S 



by those erected from B\ resulting in M. Take a tracing of H and place it as shown 
by H* and obtain H\ Take a stretchout of H'' and place it on hi, and obtain the patterns 
from intersections on M and L at a right angle to i-i. If 1-2 in both J and / in eleva- 
tion were allowed to stand at a right angle to the rake, a simpler method could be em- 
ployed for obtaining the patterns using but one profile, the principles being similar to 




I lJ C mfmiiiiiimmmiM^ 




3-12 1 1 



Fig. 9^ 



that given in Fig. 91. At a right angle to F5 in Fig. 92. from points F and 5°, the hues 
FA' and 5°B' are drawn equal to iB in plan, resulting in the true angle A'ST's- Next 
place the profile W as shown in the true 'angles by H'\ A stretchout of this profile is 
then placed on rs and the pattern obtained from intersections on n-m and 5-0, which 



TEXT BOOK ON PATTERN DRAFTING 69 

gives the pattern for the middle moulding. The lower miter pattern H and upper one 
K, previously obtained from similar letters, are correct, but the upper miter pattern 
/, for the piece HI and lower miter pattern J for the piece KJ, must he traced from the 
patterns obtained from 5-0 and n-m respectively in the true angles. 



PATTERN FOR HIP RIDGE 

FIGS. 93 and 94. When patterns are to be developed for hip ridges, no matter what 
their profile, or what angle the roof may have in plan; or whether the sides of the roofs 
have equal or unequal pitches, the principles given in Figs. 93 to 95 inclusive apply 
to each case. 

In Fig. 93 is shown the elevation of a mansard roof A, with a gutter at the foot 
and a deck moulding at the top, the deck moulding having an apron attached shown by 
i in section, which miters with the hip ridge C" at c. B is the plan, a right angle as shown 
by the solid lines or an octagon angle as shown by the dotted lines. A circular comer 
piece de is attached to the ridge and apron at a and b. Having drawn the elevation 
the miter for the deck mould could be obtained direct from same, but before the pattern 
for the hip ridge can be developed, a tn.ie face of the mansard must be drawn giving the 
true angle and miter line. In practice a full elevation is unnecessary. All that is re- 
quired is the pitch of the roof as shown by DEF, and the patterns are obtained as follows : 
Take a tracing of FED and place it as shown by FED in Fig. 94, and if the plan of 
the roof is a right angle, take the length of DF and place it on the vertical line D°F°, 
and draw the lines D°A and F^B and intersect same at D° and F\ by vertical lines dropped 
from D and F in the pitch of roof. Then AD°F^B is the true face and angle. Knowing 
the profiles that the hip and apron are to have, place in position as shown by 1-2-3 
and HJ and draw the lines JI2. With / as center and the desired radius IK, draw the 
comer piece JK^. Then JKt,I is the pattem for the corner piece. For the apron H'J, 
take the stretchout of 1-2-3 ^"d place it as shown from i' to 3'. Then obtain the 
pattem shown. For the hip pattem take twice the stretchout of 1-2-3 ^^^'^ place it on 
a-b drawn at a right angle to D°F^ as shown. Draw the usual measuring lines which 
intersect as shown. Then L is the upper miter cut joining the apron and M the lower 
miter cut running parallel to the cornice line. Before bending-up this ridge in the 
brake, a true profile must be obtained. We know that the profile of the ridge on a 
horizontal plane is a right angle, but it will be more than a right angle when viewed at 
right angles to the hip Hne. The two methods of obtaining this true profile or angle 
is shown in the plan. Draw the miter line of the plan lYO and parallel to it draw RP. 
Make P/?' equal to ED in pitch of roof and draw D^R. Then RPD^ is the true elevation 
through OX in plan. At pleasure, at right angle to 0A^ draw ai, cutting OX at ;. 



70 



THE NEW YORK TRADE SCHOOL'S 



Extend cd, cutting RP at e. From e, at right angle to D'R, draw ef. Through e, parallel 
to RD\ draw hi. Take the distance jc or jd in plan and place it as shown by ec' and 
cd' . Draw a line from f to c' and d', getting the angle desired. Next take a tracing 




Fig. 93. 



of 1-2-3 ii^ the true face and place it as shown by /- 2"-3" on either side in the true 
angle. This same angle could be obtained by taking the distance ef and placing it as 
shown by jf in plan and drawing lines from /' to c and d. 



TEXT BOOK ON PATTERN DRAFTING 




TRUE FACE FOR 
OCTAGON PLAN 



Fig. 94. 



72 THE NEW YORK TRADE SCHOOL'S 

Using the same pitch of roof, develop the patterns for the apron and hip, when 
the plan of the roof is an octagon, as shown in plan A', Fig. 94. In this case DF 
is placed as shown by D^F^, and D"" and T'^, obtained from 5 and T in plan. The half 
profile of the ridge is placed as shown by i°-2°-3° and the patterns developed as before. 
The true angle of the octagon hip ST is obtained by drawing ST'; make S^D^ equal 
to DE in pitch of roof and draw D'T'; n-m is extended to 0, from which or is drawn 
at a right angle to tlie hip. or is then placed in plan from r' to 0' and the true angle ob- 
tained. 

FIG. 95. In this connection it may not be out of place to apply these principles 
to roofs having unequal pitches, as shown by .4 and B in Fig. 95. C is the elevation. 
Draw the miter line DE and draw a'c parallel to it. Make a'h' equal to ah. Draw h'c. 
Draw at pleasure and at a right angle to DE the line cd, extending same to e, from which 
point draw ef at right angle to b'c. With e as center, draw the arc fh, and from h 
parallel to cE draw hi, which is the same as if we had taken the distance from e to j 
and placed it as shown from j to / in plan. Draw a line from ;' to c and i to d. Then 
cdi is the true angle. In obtaining the miter patterns for the apron and hip ridge, true 
faces would have to be obtained for each side having a different pitch, in the same 
manner as shown in the true face for square plan in Fig. 94 ; the patterns for the aprons 
are obtained as there shown, but only the pattern for the hip ridge for each side is necessary, 
because each side has a different pitch in Fig. 95. After obtaining the true angle in Fig. 
95, the patterns can be omitted. 



FINDING TRUE ANGLES IN IRREGULAR PIECED ELBOWS 

FIGS. 96, 97 and 98. When patterns are desired for irregular pieced elbows, the 
difficulty does not lie in preparing the patterns, but in obtaining the true angles. Fig. 
96 is an example that is apt to arise in furnice piping, blower pipes, etc. The pipe A^ 
leaves the furnace top at an incline, but on a horizontal line .4 in plan. The second 
section of the elbow B^ not only inclines in elevation as shown, but also away from the 
horizontal as indicated by B in plan. The upper section is vertical as shown by C in 
elevation and C in plan. The problem is to find the true angles between the first and 
second sections and between the second and third sections. After the true angles are 
secured the elbow patterns are developed in the usual manner, and a slip joint placed 
in the second section, as shown by a-b which will allow the upper elbow to be turned 
upon the lower one, until their correct relative positions are obtained. The method 
of obtaining these true angles is shown in Fig. 97, in which .4 and B represent respec- 
tively the elevation and plan of portion of the furnace hood. When obtaining these 
true angles it is only necessary to deal with the center lines after which the half diam- 



TEXT BOOK ON PATTERN DRAFTING 



73 



eter of the pipe is placed on either side and the miter Hne obtained. Therefore we will 
assume that C in elevation is the point where the center of the pipe will come, that length 
will equal CD and have a rise equal to ED, leaving the furnace in plan on a horizontal 
radial line shown by C°D°. The second section of pipe has an incline equal to DF, 
with a rise equal to GF, but is brought forward a distance equal to HF° in plan, as shown 
by D°F°. The third section of pipe rises in a vertical line FK in elevation and is shown 
by the dot F° in plan. For the true angle of KFD in elevation, draw any line parallel 



(example) 





Fig. g6. 



and equal in length to D°F° in plan, as shown by D^F\ Erect the perpendicular from 
F' making F'F^ equal to GF in elevation. Draw D^F'^K\ which is the true angle for 
similar letters in elevation. On either side of D^F'^K^ place the half diameter of the 
pipe, draw the miter line ab and develop the patterns in the usual manner. For the 
true angle of CDF in elevation, take the distance from C° to F° in plan and place it as 
shown by C°F° in Fig. g8. Erect the vertical line F°F equal to '7^ in elevation in Fig. 
97 and draw a line from F to C° in Fig. g8. This line then represents the base of the 



74 



THE NEW YORK TRADE SCHOOL'S 



angle to be obtained. As CD in Fig. 97 is the true length of the first section and D'^F'^ 
the true length of the second section, it is only necessary to take the distance of CD 
as radius and with C° in Fig. 98 as center, describe the arc D, which then intersect by 
an arc struck from F as center, the radius being F^D' in Fig. 97. Draw the angle FDC° 



ELEVATION OF 

CENTER LINE 

OF ELBOW 




(E3X) 



C 




Fig. 97. 



Fig. 98. 



in Fig. 98, which is the true angle for similar letters in elevation in Fig. 97. The pipe 
is now constructed around the true angle in Fig. 98 and the miter line ab, and patterns 
obtained in the usual manner. The method of obtaining the pattern between the conical 
hood A and round pipe in Fig. 97 will be described in Part Two. 



TEXT BOOK ON PATTERN DRAFTING 



75 



FIGS. 99, loo and loi. Applying the principles of the preceeding problems, next 
obtain the true angle of an elbow turning around a building whose corner is square as 
shown in the example in Fig. 99, by A-B. The pipe C has an angle indicated by a and 
the pipe D an angle indicated by b. It is immaterial what angle the wall may have in 
plan, the principles are similar. 



(example) 




Fig. 99. 



---■1°' 





Fig. ioi 



In Fig. 100 is shown the plan and elevations. ABC represents part plan of pipes. 
Draw the center line and locate at pleasure the points D and F. D°E° in the side eleva- 
tion shows the true length and pitch of DE in plan, and fi'F' in front elevation the true 
length and pitch of EF in plan ; E^D"^ in front elevation is equal to aD° in side. Know- 
ing the true lengths, the true angle is found by taking the distance DF in plan and 
placing it as shown by DF in Fig. loi. From D erect DD^ equal to fcZ?" in Fig. 100. 
With D°E° in side as radius and £)' in Fig. loi as center draw the arc E", which inter- 
sect by an arc struck from F as center and F'ii^ in Fig. 100 as radius. Then will D^E^'F 
in Fig. IOI be the true angle. The pipe is then placed in position and the miter line a-b 
drawn as shown. 



76 THE NEW YORK TRADE SCHOOL'S 



PATTERNS FOR HIPPED SKYLIGHT 

FIGS. I02, 103, 104, 105, 106 and 107. In Fig. 102 is shown the method for obtain- 
ing the patterns for a hipped skyhght with ventilator. These same principles are appli- 
cable to skylights having single or double pitches with or without \-entilators. The 
method of computing the lengths of the hip, common and jack bars in various sized sky- 
lights when the curb measure is known, will also be explained. The skylight drawings 
are one-fourth full size or three inches to one foot, so that when the full size patterns 
are developed they can be used in shop practice. In obtaining the length of the warious 
bars, measurements are taken upon the glass line, so that the size of the glass can be 
obtained and cut, before the skylight is set together, which avoids unnecessary delay. 

The usual pitch for hipped skylights is one-third the span. In other words, if the 
run is 6 feet, the rise will be ^ or two feet. Knowing the pitch wanted (in this case 
one-third) proceed to draw the half section as follows: Draw the center line CA^ at right 
angles to which, from A, draw AB equal to 12 inches; make AC 8 inches or one-third 
of 2 X 12, and draw CB. Draw the lower curb B as shown, also the upper bar E, 
and place in the position shown the profile of the common bar D. Complete the ven- 
tilator as shown by the sections F and G, also the section of the brace H. If no ven- 
tilator was wanted, the ridge bar J would be placed in the position shown, by tracing 
E on either side of the center line. For the common bar pattern take the stretchout 
of D and place it on the line a-b as shown, and draw the usual measuring lines which 
are intersected by lines drawn from B and E, resulting in the pattern shown. When 
measuring the length of the common bars, line 2 in the pattern is used, because the 
hypotenuse of the triangle CBA falls upon line 2 in the half section. To obtain the pat- 
terns for the hood G, brace H, outside vent F, and inside vent E, take stretchouts of 
each of these parts and place them on the vertical line cd, as shown in Fig. 103. Draw 
measuring lines as shown and intersect same by taking the various distances from the 
center line in the half section in Fig. 102 to the different points in the ventilator, and 
placing them on either side of the center line cd in Fig. 103. Then G\ H\ F\ E^ are 
the patterns for the parts having similar letters in the half section in Fig. 102. The 
arrow points on the patterns in cd in Fig. 103 indicate where measurements must be 
taken when laying out ventilators for different size skylights. The pattern for the 
curb in Fig. 102 is obtained by taking the stretchout of B and placing it on hi as shown, 
after which the measuring lines are intersected by lines dropped from B. The letters 
e and / in the pattern B° indicate where the holes should be punched to allow the inside 
condensation to escape to the outside at 4 in B. The measuring line in B° is indicated 
by the arrow. Before the pattern for the hip bar can be obtained, a plan view must 



TEXT BOOK ON PATTERN DRAFTING 



77 



be drawn as shown. As the plan of the skyHght is to be square, the hip line A'B' is 
drawn at an angle of 45°. If the plan of the skyHght were other than a right angle, the 



^.-ui^-K ,...;ii 




76 



THE NEW YORK TRADE SCHOOL'S 




TEXT BOOK ON PATTERN DRAFTING 77 

be drawn as shown. As the plan of the skylight is to be square, the hip line A '5' is 
drawn at an angle of 45°. If the plan of the skylight were other than a right angle, the 
pattern for the hip would be developed in precisely the same way as that which will 
follow, bearing in mind that the miter or hip line would be the bisection of the given 
angle, as shown by RSTU. From the various intersections in B and E in the half section 
drop lines intersecting the hip line in plan as shown, from which points horizontal lines 
are drawn as shown, completing the quarter plan. A profile of the common bar D is now 
placed on the hip line A'B^ in plan, as shown by D°, so as to obtain the horizontal meas- 
urement. Through the small figures in one-half of D°, lines are drawn parallel to A^B\ 
intersecting those previously dropped from B and E in the half section, and resulting 
in the points of intersections i to 6 in i?' and i to 6 in .4'. Parallel and equal to A^B^ 
draw A-B-, making A^C^ equal to AC in the half section. Draw a line from C'^ to B-. 
From the various intersections in plan i to 6 at the curb and i to 6 at the ridge, erect 
lines indefinitely as shown. Measuring from the line AB in the half section, take the 
various heights to points i to 6 in B and E and place them on similar lines erected from 
plan, measuring in each instance from the line A^B' in the hip section, and resulting 
in the points of intersections i' to 6' in B- and i" to 6" at the top vent ridge. Connect 
the similar points by lines as shown, which, if correct, must run parallel to C^B'. This 
then represents the true section on the hip line in plan. The true profile of the hip bar 
is found by placing a duplicate of D as shown by D"^ and perpendiculars drawn, inter- 
secting similar lines in the hip section. By connecting points as shown by K, the desired 
profile is obtained. The pattern for the hip could be drawn at a right angle to I'-i", 
but for want of space it has been transferred as shown by A'' in Fig. 103. Take the stretch- 
out of K in Fig. 102 and place it on m'-n' in Fig. 103 as shown. Draw the usual meas- 
uring lines as shown. Now draw at pleasure in Fig. 102 the two perpendiculars in the 
hip section, shown by m-n and rs. With the dividers, take the various distances from 
m-ii to points i" to 6", and place them in 7\' in Fig. 103 on similar lines, measuring from 
m'-n'. Make the distance between the lines m'-n' and /-s' equal to the distance be- 
tween similar lines in the hip section in Fig. 102. Measuring from r-s take the various 
distances to i'-6' and place them on similar lines in Fig. 103, measuring from r's'. 
Trace lines through these points, which gi\'es the pattern for the hip bar. The aiTow 
points indicate the measuring line. The last pattern is that of the jack bar, shown in 
Fig. 102. Take a tracing of D and place it in any position horizontally in plan, as shown 
by D^'. Through the various points in D^', draw horizontal lines, intersecting similar 
numbered lines in the hip bar in plan as shown from i^' to 6^' and i^' to 6"'. From these 
intersections lines are carried into the half section, intersecting similar lines, resulting 
in the points of intersections i'' to 6^' and i"'' to 6"', from which, at right angle to 
CB, similar lines are intersected in the pattern D' by dotted lines, as shown by similai 
numbers. This gives the pattern for the upper cut of the jack, the lower cut being 
similar to that shown on the common bar. If a ridge bar is desired in place of the 



78 



THE NEW YORK TRADE SCHOOL'S 



ventilator, the pattern shown by £' in Fig. 103, could be used, simply dupli- 
cating £' opposite the line ef, so as to form up the profile J in the half 
section in Fig. 102. In using a ridge bar, the common and hip bars are 
sometimes attached in a manner shown in Fig. 104. A is the ridge bar in- 
tersected by the two hips B and B and requires a miter cut 2-t. The miter 
cut 2V is shown in Fig. 103 in the pattern A'' from v to iv. For the cut it in 
Fig. 104 it would only be necessary to draw a horizontal line from 2 in plan in Fig. 102, 





PATTERN FOR 
HIP BAR 




PATTERNS FOR VENT. 



Fig. 103. 



as shown by 2t, and where this line intersects the various lines in the half hip, project 
lines at a right angle to the hip line, and intersect similar numbered lines in the hip 
section. Measurements are then taken from the line m-n to these points and trans- 
ferred to the pattern A'' in Fig. 103 on the opposite side of vw. While this pattern has 
been omitted for want of space, the student should project these points to his pattern 
on the full-size drawing. When the common bar C in Fig. 104 intersects the two hips 



TEXT BOOK ON PATTERN DRAFTING 



79 



BB, the cuts 2a and 2a are similar to the miter cut shown from i''' to 6™ in the pattern 
D'^ in Fig. 102. If the center of the common bar D in Fig. 104 were attached, as shown 
at 2, then the cut 2c would be the same as xy in /?' in Fig. 102 and 2b in Fig. 104, the 
same as 1^-6^' in D' in Fig. 102. To illustrate the rule for obtaining the lengths of 
the various bars in any given size skylight, Figs. 105 to 107 have been prepared. Take 
a tracing of ABC in the half section in Fig. 102, and place it as shown by ABC in Fig. 
los- Divide AB into inches, half inches and quarter inches, and erect vertical lines 
cutting BC as shown. This triangle is then used for obtaining the true lengths of jack 
and common bars. In similar manner take a tracing of A^B'C in the section on hip 





OBTAINING FULL SIZE MEASUREMENTS FOP 
JACK AND COMMON BARS. 



Fig. 105. 



in Fig. 102 and place it as shown by similar letters in Fig. 106. As A-B- represents 
the plan of the hip bar, whose common bar measures 12 inches in plan, then divide A'B'- 
into twelve equal parts as shown, and project lines upward intersecting B'C" as shown.' 
This triangle will be used for obtaining the length of the hip bar. Assume that two 
skylights are to be constructed, the curbs being 4x8 feet as shown at A in Fig. 107, 
one without a ventilator as shown by the solid line, and one with a ventilator 6 inches 
wide, as shown by the dotted lines. Knowing the size of the curb, the pattern shown 
by B° in Fig. 102 is used, measuring from the arrow points. To obtain the lengths 
of the ventilator, ridge, common, jack and hip bars the following methods can be 
employed, no matter what size the skylight may be. In the following rules 5 will indi- 
cate the shortest side of curb, L the longest side and V the gi\'en width of the ventilator. 
Rule I. To obtain the true length of the ridge bar. 

L — S = length of ridge bar. 



8o THE NEW YORK TRADE SCHOOL'S 

Rule II. To obtain the true length of the ventilator. 
L ~ S + V = length of ventilator. 

Rule III. To obtain the measuring lengths of the common and hip bars when no 

ventilator is used. 

5 

— = measuring length for common and hip bars. 

Rule IV. To obtain the measuring lengths of the common and hip bars when a 

ventilator is used. 

S - V 

— = measuring length for common and hip bars. 




obtaining full size measurements for hip bars 
¥k. io6. 



To obtain the measuring length of the jack bar use dimensions in diagram as given 
in Fig. 107. The first step in applying the foregoing rules is to make a diagram as shown 
at A, giving the size of glass and divisions of the bars. Then the length of the ridge 
bar a would be 8 feet — 4 feet = 4 feet, to be measured from the arrow points in £' in 
Fig. 103. The length of the ventilator in .4 in Fig. 107 would be 8 feet — 4 feet = 4 feet + 6 
inches = 4 feet 6 inches, to be measured from the arrow points in E' in Fig. 103. The 
length of F' would be 4'-6i" and the hood G^, 4'-9", because F and G in the half sec- 
tion in Fig. 102 project over E, \ and li inches respectively. Referring to A in Fig. 107 
the measuring lengths of the common and hip bars, when no vent is used, would be 
4 feet ^2 = 2 feet. As AB in Fig. 105 equals i foot, then for 2 feet the length of 
the common bar would be twice CB, measuring from arrow points in the pattern for 
common bar D' in Fig. 102. Using the same measuring length, the hip bar would be 
twice C'B^ in Fig. 106, measuring from arrow points in /C' in Fig. 103. If a 6-inch vent 
was employed, as shown in Fig. 107, the measuring length would be 4 feet — 6 inches 



TEXT BOOK ON PATTERN DRAFTING 



8i 



= 3 feet 6 inches h- 2 = i foot 9 inches. The true length of the common bar would 
then be equal to CB in Fig. 105 plus the distance aB, which is found by erecting the 
line from 9 to a. The true length for the hip bar would be found by taking the dis- 
tance OB"^ in Fig. 106 plus aB\ As the dimension of the jack bar in Fig. 107 is i foot 
4 inches, the true length is found by taking the distance CB in Fig. 105, and adding 



\ 18" 


18" 


16" 


16" 


16" 


/ 16" 


"V:l 


~~a,~' 


-^,7 


--/ 






/~~' 


b 


T 


-\ 




c/ 




\16" 


/ 


d 








\ 



\ 




/ 18" 


\ 18 
IB" \^ 



Fig. 107. 



to it, the distance hB, which is found by erecting a line from 4. This length is then 
measured from the arrow points in the pattern for jack bar D^ in Fig. 102. If desired, 
all the glass can now be cut, before the skylight is set together, the length of the 
glass being equal to the length of the bar, and the width equal to the dimensions in 
Fig. 107, minus \ inch in length and width for play room. 




Fig. 108. 



FIG. 108. Make a new drawing of the half section in Fig. 102 without a ventilator, 
and develop the pattern for a valley bar only, as shown in the reduced plan in Fig. 
108. Compute the lengths of the common and hip bars in the skylight, the size of 
which is shown at B in Fig. 107, one without a ventilator and one with a ventilator 
9 inches square. Find the lengths of the various pieces in the ventilator. 



THE NEW YORK TRADE SCHOOL'S 



PART TWO — THE PRINCIPLES OF RADIAL LINE 
DEVELOPMENTS 

FIGS. 109, no and in. By radial line developments we mean patterns that have 
been developed by means of radial lines, converging to a common center. The forms 
or shapes considered within this part have for their base either the circle, figures of equal 
or unequal sides, or any of the regular polygons that can be inscribed in a circle, the 
lines drawn from the corners of which would terminate in an apex or point, directly 
over the center of its base as shown in Figs. 109 and no. In Fig. 109 ABCD repre- 
sents the base of a circle, the center E coming directly under the apex F. Knowing 
the height of the axis EF, all lines drawn from either of the points in the circle as A, 
B, C and D, will terminate at F as shown, and all lines will be of equal length and pitch 
because the apex F appears directly over the center point E. This is equally trae when 






Fig. 109. 



Fig. no. 



Fig. III. 



a frustum of a cone is employed, as shown by ahcd, the pitch and length of the lines 
Fa, Fb, Fc and Fd being equal. What is true of the circle is also true of any other 
figure the base of which can be inscribed in a circle. In Fig. no a pyramid is shown, 
the base ABCD being square and the axis equal to EF. In these cases all lines drawn 
from the corners also terminate at the apex F. The length of any one of these lines 
becomes the radius by which to strike the pattern, but Fj represents the true length of 
the pitch at right angle to the base AB, while ef would be the true pitch if a frustum 
was desired, as shown by abed. Fb and FB would be the radii with which to describe 
the frustum. There is still another figure which should be considered in this part, 
and while its base is not a true circle, it is composed of arcs of circles, shown by the 
elHpse in Fig. n i ; a being the center from which the arc be is struck, and d the center 
from which be is struck. The principle in this figure is the same as in Fig. 109. In 
Fig. Ill df is the axis of the larger curve, and fc or fb the radius by which to strike the 
•1 ittern, while ai is the axis of the smaller curve, and ih or in the radius by which to 



TEXT BOOK ON PATTERN DRAFTING 83 

strike the pattern. The patterns for another figure known as the scalene cone, can also 
be developed by means of radial lines, although its apex is not directly over the centei 
of its base. This figure will be considered in Part Three. 

When obtaining patterns for tapering forms the following rules should be employed. 

(i.) There must be an elevation, section or other view, showing the true height 
of the axis, see a A in Fig. 112, and the true length of the radius with which to strike 
the pattern as shown by AB or AC. 

(2.) A plan must be drawn from which the stretchout can be obtained as shown 
by B'C\ 

(3.) This stretchout, if measured along the plan of the base as shown, must be 
laid off on the arc i-i' in the pattern, which represents the base; or if measured along 
the plan of the top as E^D\ it must be laid off on the arc drawn from ED in eleva- 
tion, as DF. 

(4.) Should a curved, irregular or straight Hne be drawn through any cone, as 
illustrated by the straight Hne a-b in Fig. 114, and which the radial lines in elevation 
will intersect, then, from these intersections on a-b, lines must always be carried at 
right angles to the axis .4-4', until they intersect the true length used to describe the 
pattern, as shown from i to 7 on A-f. With A as center, the points of intersections are 
then carried to similar radial lines in the pattern, as shown from 7"" to 7". 

(5.) When obtaining the true section on any curved or straight line as a-b in 
Fig. 114, which is not at a right angle to the axis line, the shape of the section when 
developed will be different in shape from that shown in the plan for base, and must 
be obtained as indicated in the illustration. This will be explained in detail in the 
problems that follow. 



PATTERN FOR A RIGHT CONE 

FIG. 112. First draw the center line A-j, upon which place the height of the 
cone as Aa; through a draw the horizontal line BC, making aC or oB equal to one- 
half width of the base, and draw lines from B and C to ^4. Then AC or AB is the radius 
with which to describe the pattern. In practice the half elevation only is required. 
Directly below the elevation, draw the plan of the base B^C\ which is divided into equal 
spaces shown from i to 12. The radial lines drawn in plan and elevation are not 
necessary, but are shown to make clear their relation to each other. To obtain the 
pattern for the cone, use A as center, and with AC as radius, describe the arc i-i'. 
From I draw a line to A, and set off on i-i' the stretchout of the base B^C\ and draw 
a line from 1' to A. Then A-i-i' is the desired pattern for the cone. If a frustum 
of a cone is desired, as shown by BCDE, then using AD as radius the arc DF would be 
drawn, making D-F-i-i' the desired pattern. £'D' represents the section of the top 



84 



THE NEW YORK TRADE SCHOOL'S 



in plan. Using the same plan and elevation as in Fig. 112, develop the pattern for 
the frustum of a cone EDCB when made of ^-inch metal. In this case the same rule 
is used, as given in Fig. 10. On HJ in Fig. 112 the regular stretchout is laid oft", to 
which 7 X i is added, as indicated by Hm, and the required stretchout obtained, as 
shown from J to i'. This is then laid off on the arc i-i', as shown by the dots 2'-i'-/^- 
^', etc. 




Fig. 112. 



FIG. 113. Obtain the pattern for the lower flare a of the ventilator A, the half 
plan being shown l)y bed. Also obtain the pattern in one piece for the hood B, pitched 
as shown in end view, with semi-circular ends ec. By the same rule, obtain the pattern 
in one piece for the hood C, the top of which is rectangular, the base having rounded 
comers as shown by abed. S indicates the seams. 



TEXT BOOK ON PATTERN DRAFTING 



85 



PATTERN FOR FRUSTUM AND SECTION OF RIGHT CONE 

FIG. 114. Shows the method of obtaining the frastum and section of a right cone 
when the upper plane a-b is oblique to the line of its axis. First draw the elevation 
of the cone A-i'-j' and directly below it the plan view on the line I'-j'. Divide the 
plan into equal spaces as shown by the small figures i to 7, and tlraw radial lines to 





^•^^ 




[/ 


a 


\| 


\_ 


1 


/ 



FRONT 
ELEVATION 




C (E4X) 



Si c 



Fig. 113- 



the center A\ From the various intersections i to 7 erect lines intersecting the base 
of the cone from i' to 7', and from the latter intersections draw lines to the apex A. 
Let ab represent the plane drawn oblique to the axis of the cone, which also inter- 
sects the radial lines from i to 7. Using A as a center and with A-j' as radius, describe 
the arc 7"-7", upon which the stretchout of the plan is placed, as shown by similar 
numbers on the arc 7"-7". From these points draw radial lines to A. From the 
various intersections on a-b at right angles to the axis line, draw lines as shown, cut- 
ting the line A-j' from i to 7. Then using A as center with radii equal to the various 
divisions as Ai, A2, A3, etc., draw arcs, intersecting similar radial lines in the pattern 
giving the intersections 7"^ to 7''. A line traced through points thus obtained as shown 
by 7''-7"-i"-7"-7>^-i^-7^ will be the desired pattern. If the pattern or true section 
was desired so as to close the top ab in elevation, whether the line were curved as shown 
by m-n in Y or vertical as shown by st in A', the same principle would be employed 



86 THE NEW YORK TRADE SCHOOL'S 

as that used in obtaining the section on a-b. From the various intersections i to 7 
on a-b, drop vertical hnes, intersecting similar radial lines in plan as shown from 1° 
to 7°; to obtain the point 4°, a horizontal line is drawn through 4, until it intersects 
the side of the cone at d, from which point it is carried vertically to the plan, inter- 




FiG. 114- 



secting the center line 1-7 at d'; then using A^ as center describe the arc cutting the 
radial line 4-4 at 4°-4°. Next take the stretchout of a-b and place it on the center line 
1-7 extended in plan as a'b'. At right angle to a'b' through the various points, draw 
vertical lines, which intersect by horizontal lines drawn from similar points 1° to 7° 
in plan, and resulting in the pattern Z. In Fig. 114 obtain the developed sections 
only for the vertical plane st in X and the curved plane ni-n in Y, using the method 
shown in getting out the pattern Z. 



TEXT BOOK ON PATTERN DRAFTING 87 

FIG. 115. Develop the pattern for the head mnor in Fig. 115, shown in plan by 
aebcfd. Di-aw the center line Sm and extend no obtaining t, which is the center point 
from which to strike the pattern. Develop this pattern below the plan, placing on 
the outer arc twice the girth of ac in plan. 

FIG. 116. Develop the patterns for the foot and body of a hip bath, shown in 
Fig. 116 by abcdfh, the outline being indicated liy be, which is drawn at pleasure. The 
centers are represented by / and i from which points strike the patterns. The plan A 
represents a section through dc. Vertical lines are erected from the plan, cutting dc 
as shown, and from these intersections lines are drawn radially from j, cutting be, 
from where they are carried at a right angle to the center line until they cut the side 
be; then proceed as shown in Fig. 114, placing the patterns in any convenient position 
in Fig. 116. 



ELEVATION 




(E 2X) 




lj\i I i/ii 

\ I / 'I 

|\ I /i II 

'! I ! 'I 




FIG. 117. Obtain the pattern for a tapering collar efed in Fig. 117, when the roof 
has a single pitch as shown by AD, also when it has a double pitch shown by FED. 
a-b represents the center line of the collar, b being the apex of the cone and B the half 
section on the line cf. 

FIG. 118. Develop the pattern for a conical boss shown by EFGH, AB representing 
the part plan of the can, while EHLJ shows the half section on the line EH. DC 
shows the center line through the boss, and C the center from which the arc AB is stmck. 

FIG. iig. Develop the patterns for the double scale scoop HEFGDJ. It is to be 
cut from the two cones ABCD. Apply the method used in Fig. 116. 



THE NEW YORK TRADE SCHOOL'S 



PATTERN FOR SQUARE PYRAMID 

FIG. 1 20. Shows the development of a pattern for a square pyramid; this prin- 
ciple is applicable to the various shaped ornaments arising in cornice work or other 
articles in the sheet metal line. First draw the center line Aa, and set ofif the distance 
aC and aB and draw the elevation ABC. In its proper position draw first the plan, i, 




Fig. ny. 



2, 3, 4, and then the miter lines 1-3 and 2-4. AB or AC represents the true length 
on a'b in plan, but the true length on a'-2 in plan must be found, by erecting the per- 





pendicular a' A'- equal to the vertical height aA in elevation. The line A^2 then repre- 
sents the true length or radius with which to develop the pattern. With any point 



TEXT BOOK ON PATTERN DRAFTING 89 

as A ^ as center, describe the arc I'-i". Set the dividers equal to the spaces in plan and 
step off on the arc I'-i", the divisions shown by 2'-3' and 4' and draw lines to the apex 
A\ Connect lines with the outer corners, then will i'-2,'-i"-A'' be the desired pattern. 




Fig. 120. 

FIG. 121. Using the same rule given in the preceding problem, develop the pat- 
terns for the pyramids shown in Fig. 121. All elevations are to be similar to ABC 
and the plans as shown by D, E, F, G and H. Note that all of these plan views are in- 
scribed in circles, and the lines drawn from the corners of same, terminate in an apex, 
directly over the center of their base. Each plan is to have a separate elevation, with 
a vertical height equal to yla. The radius with which to develop the patterns is ob- 
tained in each case by placing the vertical height A a at a right angle to the miter Hne 
in the various plans, as shown by a' , a", a'", a° and a^. AX' represents the line in 
elevation on the corner A' in plan H. The center point in the plan D can be ob- 
tained by bisecting bd, and obtaining e, through which draw a line towards / until it 
intersects the center Hne Ad. The shaded section in each plan represents the true sec- 
tions on the respective miter hnes. 



PATTERN FOR FRUSTUM AND SECTION OF SQUARE PYRAMID 

FIG. 122. Draw the plan and elevation of a square pyramid, similar to Fig. 120, 
and develop the pattern as shown on that plate. Draw the oblique plane de and ob- 
tain the frustum as follows: From the intersections d and e, drop vertical lines, inter- 



9° 



THE NEW YORK TRADE SCHOOL'S 



secting similar lines in plan as shown by the shaded portion. With a' as center and 
a'i° as radius, describe the arc cutting 2-4 at i. Erect the perpendicular from i, cutting 
A^2 at i''4''; also from 2° erect a line cutting A^2 at 2''3''. Then ii"^ and 2°-2'' will equal 
rd and se respectively in elevation. Using A- in the pattern as center, and with A'- 
2^2,^ and A^-1^4^ as radius, intersect similar lines in the pattern and obtain points of 
intersections i'', 2^, 3^, 4^^, i". Then I'-i^-i^-i" will be the pattern for the frustum. 
The true section on de is obtained by taking this distance and placing it on any line as 
de in Fig. 122, making 62°, C2,° and di° and ^4° equal respectively to a' 2°, a' t,° and the 
distance from the center line to 1° and 4° in plan in Fig. 120. 

FIGS. 123 and 124. Obtain the frustum and section of the hexagonal pyramid 
shown in Fig. 123, in which ABC represents the elevation cut by the oblique plane 
DE. The plan view on the base line is shown and the horizontal section through ED 
appears shaded. The intersection between the plane ED and the center miter line 
a'" is shown in plan by a'-a" and is obtained by projecting a horizontal line to a on AC, 
then to a in plan, then to a' and a" as shown by the semi-circle. The true length on the 
hip line in plan is obtained by taking the distance ed and placing it as shown by c'd' , 
then obtaining A°. From the various intersections on ED, lines are projected to A°d' . 
The pattern for the frustum is shown in Fig. 124, the various radii in Fig. 123 on A°d' , 
being used and intersecting similar miter lines in Fig. 124. The true section on ED in 
Fig. 123 is shown by E°D°. 




Fig. 122. 




TRUE SECTION 

(E3X) 



Fig. 123. 



FIG. 125. Obtain the frustum and section of a pyramid when the plan is irregular 
as shown. The center point i in plan is obtained by bisecting ac by the line ef. In 
this case AC shows the true length of the hip, because it lies in a horizontal plane in 



TEXT BOOK ON PATTERN DRAFTING 



91 







U 3X) 




Fig. 121. 



92 THE NEW YORK TRADE SCHOOL'S 

plan as shown. The patterns for the frustum and section are developed, as shown by 
similar reference letters. 



PATTERN FOR ELLIPTICAL FLARING ARTICLE 

FIGS. 126 and 127. Show the method of developing the pattern for an elliptical 
flaring article. These principles are applicable to any shape or form constructed of arcs 
of circles. Draw the plan view according to the rule given in Figs. 8 or 9 in Part One 
and obtain the centers A, B, A\ B' in Fig. 126. Draw the elevation CDEF and obtain 






\ 



\ 
\ 



\ 



ELEVATION >.H 





Fig. 126. 



Fig. 127. 



the radii with which to strike the pattern, by taking the distances in plan B-i, and 
A-s, and placing them in elevation as shown, respectively by E-i' and £-5'. From 
i' and 5' erect perpendicular lines, a and b, which intersect by the flare EF extended, 
at H and J. Then JE is the radius with which to strike the pattern for that part shown 
by 9-5-A in plan, and HE the radius for that part shown by 1-5-^ in plan. With JE 



TEXT BOOK ON PATTERN DRAFTING 



93 



as radius and J in Fig. 127 as center, describe the arc 9-5. Starting at any point as 9 
set off on 9-5 the stretchout of 9-5 in plan in Fig. 126. Draw Unes from 5 and 9 to 
J in Fig. 127. Then with HE in Fig. 126 as radius and 5 in Fig. 127 as center, de- 
scribe an arc, cutting 5-^ in H. Using the same radius and H as center, draw the arc 
5-1, on which lay off the stretchout of 5-1 in plan in Fig. 126. In Fig. 127 draw a Hne 
from I to H. Now, with radii equal to JF and HF in Fig. 126 and with centers J and 
H in Fig. 127, describe the arcs Fa and aF°. FF°E°E is then the half pattern with 
seams at i and 9 in Fig. 126. 

FIG. 128. Solve the problem shown in Fig. 128, the plan of which is an egg-shape 
oval; the elevation is shown by A, the plan by 5, and the various radii with which to 
develop the pattern by CD. In striking the pattern have the seam come at 5-5 in plan. 




3 X) 



PATTERN FOR TAPERING ELBOW, ROUND IN SECTION 



FIGS. 129 and 130. The former illustrates the method of obtaining the patterns 
for a three-pieced tapering elbow, which, when completed, will appear at an angle of 
90°, as shown in Fig. 130 by dotted line through center. The method here explained 
of finding the true miter lines and developing the patterns in Fig. 129, apply to any 
pieced tapering elbow, no matter what degree it may have. First draw the elevation 



94 



THE NEW YORK TRADE SCHOOL'S 



of the frustum of a cone from which the several pieces are to be cut, as shown by A BCD. 
Extend the sides until they meet in the apex E. On DC, with F as center, draw the 
half section of the pipe as D4C. Divide this half section into equal spaces, from which 
points erect perpendicular lines, cutting the base DC as shown. From the intersections 
on DC draw lines to the apex E. The elbow in this case is to consist of three pieces 




(E3X) 



Fig. I2g. 



with an angle of 90° on its center line when completed. Then following the rule given 
in Fig. 6, Part One, for obtaining the rise of the miter lines in pieced elbows, we have 
2 2^° for the rise of the miter line, because 90 divided by 4 equals 2 2 A. Now set the 



TEXT BOOK ON PATTERN DRAFTING 95 

protractor on the center line in Fig. 129 and draw a line from the center F through 22^° 
as shown by Fd. This is all that is required so far as the miter line is concerned. As 
we do not know the length each piece will have in the throat, the correct length of each 
piece on its center line can be accurately ascertained as follows : As the end pieces in elbow 
work count one, and the middle sections two, we have in a three-piece elbow, the number 
4. Divide the center line HF in four equal parts as shown by a-h and c. Through a, 
parallel to Fd, draw the miter line KJ. In similar manner through c, but in the oppo- 
site direction, draw the miter line LM. This miter line LM is obtained by simply trans- 
ferring the angle as follows: With a as center and any desired radius, draw the arc ej; 
again using the same radius, with c as center, draw the arc f'e', making the distance 
fe' equal to fe, and draw a line through e'c and extend same either way, until it inter- 
sects at M and L. Where the radial lines intersect these miter lines, lines are drawn 
at right angles to the axis until they intersect the line BC from i to 7 and i' to 7'. The 
development of the pattern now becomes a simple matter, the principle being similar 
to that given in Fig. 113. In Fig. 129 i-N-0-i° is then the pattern for the lower section 
of the elbow; NRPO the pattern for the middle section, and RSTP the pattern for the 
upper section. When the elbow is completed, it will have the appearance shown in 
Fig. 130. It should be understood that this rule can only be employed when the elbow 



has no given dimensions as regards height XH and projection FX. When these dimen- 
sions are given, the elbow can only be developed by triangulation, as explained in Fig. 
208 in Part Three. Using the same size elevation and plan as in Fig. 129, develop the 
patterns for a two-pieced elbow whose angle on its center line will be 60° when com- 
pleted. Also develop the patterns for a four-pieced elbow whose angle will be 90° when 
completed. 



96 THE NEW YORK TRADE vSCHOOL'S 



PATTERN FOR OCTAGON SPIRE ON EIGHT GABLES 

FIG. 131. Shows the principle to follow when developing the various spires on 
gables. The problem as presented is an interesting study in projections and contains 
but little in developments. Let i to 8 represent the horizontal section through AB 
in elevation, in practice the one-quarter plan only being required. Bisect each side 
in plan as shown hy F, E, C, D, G, from which points, and also the corners i to 8, draw lines 
to the center H. Next establish the height of the gables above the line AB in eleva- 
tion as shown by F^-G\ and from the center of the gables F, E, C, D and G in plan_ 
erect lines intersecting the line F'C^ at F\ E\ C\ D'- and G^ respectively. In similar 
manner from points i and 2 in plan, erect lines intersecting AB in elevation at i' and 
2'. Connect the gable lines in elevation as shown, these lines representing the extreme 
upper edge of the mouldings A and B as shown. From A in elevation, which repre- 
sents the lowest edge of the valley 8-H in plan, draw a line to C in elevation, which 
represents the highest point of the valley and ridges. The line AC^ then represents 
a vertical section of the valley line S-H in plan, when viewed parallel to 7-8. Estab- 
lish at will where the lowest point of the spire is to meet the line AC\ in this case at 
a, and draw a line to the apex J, cutting the ridge line of the gables at £\ Project 
E' of the ridge and a of the valley, cutting the ridge and valley in plan, at e and a' 
respectively. Using H as center and He and Ha' as radii, intersect the various lines, 
partly shown by <?' and a"^. From c' and a'', project line vertically cutting the ridge 
and valley lines at e" and a° respectively. Draw lines from F' to £' to e" to a° to J. 
Complete the opposite side as shown. A line drawn from e" to a would show the cut 
of one side of the spire over the gable E in plan, although not necessary in developing 
the pattern. For the pattern, use J as center, and with radii equal to JE^ and J a 
describe the arcs shown. Draw any radial line as LJ, intersecting the inner arc at £^ 
On either side of L, perpendicular to LJ, set off La" equal to L°a° in elevation, and draw 
lines from a" to E^ and J. If the whole pattern is desired in one piece, join eight pat- 
terns. When the spire is large, the pattern for one side is used, allowing edges for 
soldering. 

FIG. 132. Obtain the pattern for the spire shown in Fig. 132, which is to be 
square, fitting upon four gables. The bottom of the spire at a and b is to be in a ver- 
tical Hne over the body of the shaft A and B. After obtaining the height of the gable 
the pattern is obtained by using Dc and Db as radii; da represents the projection in 
the center of the pattern, at right angle to its center line. 



TEXT BOOK ON PATTERN DRAFTING 



97 



PATTERNS FOR FLARING STRIPS FOR A SPHERE 

FIG. 133. When obtaining the flaring strips for a sphere, the method shown in 
Fig. 133 is applicable to any size or number of pieces, in this case three in the half 




(E2X) 



Fig. 131. 




98 



THE NEW YORK TRADE SCHOOL'S 



sphere. Using A as center, describe the circle BHCN, and erect the center line AJ. 
Divide the quarter circle HC into equal spaces, and have as many spaces as there are 
flaring strips in the half sphere, as shown by D and G. Through these points draw the 
dotted lines BC, ED and FG. Now applying the same principle used in obtaining the 
frustum of a right cone, draw- lines through CD and DG until they intersect the center 









iL 








:-- 








1 \\ 
1 w 

i V\ 


PATTERN 

FOR 

X 




/ 


1 '^ '' 

1 \ ^ 
1 \ \ 
IK \ ^ 


F^ 




"X 


4— ■^\ 


E/ 


Y 




1 \Oi^ 




(E2X) 



Fig. 133. 



line at L and K respectively. L then becomes the center from which to strike the 
flaring strip for Z, and K the center for the flaring strip Y. As Z and 1' join on the 
line ED, use a as center and describe the one-quarter section as shown. Divide this 
into equal spaces as shown from i to 5. Now develop the half pattern for Z as shown 
by i-C'-C-i'; also the half pattern for Y, as shown by I'-G^-G^-i", using K^ as center, 
care being taken to place twice the stretchout of the quarter section on the inner curve 
of the pattern for Z, and on the outer curve of the pattern for Y. With HG as radius, 
describe the pattern for X as shown. 



TEXT BOOK ON PATTERN DRAFTING 



99 



FIG. 134. Obtain the half patterns of the various flaring strips for the shape 
shown in Fig. 134, the article to be constructed of four pieces as shown by EE\ DD\ 
aa! and BC. a-a' and h-b' are the centers from which the various outlines are ob- 
tained. M is the quarter section on a' -a, and N the quarter section on E^-E. The 
various radii with which to strike the flaring strips, are obtained by extending to the 
center line the lines aC, aD, DE and EA. 




Fig. 134. 



PATTERNS FOR FLARING STRIPS FOR CIRCULAR WORK, WHEN MADE 
BY HAND IN FULL CIRCLES 

FIG. 135. In Fig. 135 is shown how to obtain the flaring strip for a cove, having 
a full circle in plan when completed. A moulding of this kind would require "stretch- 
ing" along its outer edges C and D, the center portion h remaining stationary. As h 
represents the stationary point, this point can be used from which to obtain the true 
length on the flaring strip as in ordinary flaring work. The rule to be observed is as 
follows: Let CDD^O be the elevation of the cove to be "stretched" in a full circle in 
plan, the coves being struck from the centers a and a' . First draw a line from C to D 
and bisect the cove CD at b. Through b parallel to CD draw the line cd, extending it 
until it intersects the center line AB at E. Take the stretchout from 6 to C and from 
b to D and place it as shown respectively from 6 to c and from b to d. From b draw 
the horizontal Hne b-e and using e as center, describe the quarter circle 64, which 
represents the quarter section on the line eb. Divide this quarter section into equal 



loo THE NEW YORK TRADE SCHOOL'S 

spaces as shown. With radii equal to Ed, Eb and Ec, and with £' as center, describe 
the arcs d'd", b'b" and c'c". Starting from 4' on the center Hne, set off on either side 
twice the stretchout of the quarter section in elevation, and through b' and b" in the 
pattern draw radial lines to the center E\ intersecting the inner and outer arcs at d'd" 
and c'c", thus completing the full pattern. 




(E3X) 



Fig. 135- 



FIGS. 136 and 137. These figures illustrate the practical rule for obtaining the flaring 
strip when the quarter round A 5 is to be "raised." In this problem the half elevation 
only is to be drawn. Draw a line from A to B, bisect same and obtain E. From E 
at right angles to AB draw Ed, which divide into as many spaces as the radius EF con- 
tains inches. As any fractional part less than one-half inch is not taken in consider- 
ation, and as the distance FE will be 3 J inches, then divide Ed in four spaces as shown, 
and through the space nearest to the cove as o draw a line parallel to AB, intersecting 
CD at 5. Take the stretchout from d to A and from d to B and place it as shown from 
o to a and from to b. From draw the horizontal line oe and with e as center and 
eo as radius, describe the quarter section 0-5, which then divide into equal spaces as 



TEXT BOOK ON PATTERN DRAFTING loi 

shown. With radii equal to 5-6, 5-0 and 5-a, and with 5° in Fig. 137 as center de- 
scribe the arcs as shown by similar reference letters, making the girth along the arc 
0-0' equal to four times the quarter section on eo in Fig. 136. 




(E3X) 



Fig. 136. 




Fig. 137. 



I02 THE NEW YORK TRADE SCHOOL'S 

FIG. 138. When a flaring strip is desired of an ogee, having a flare in the center, 
as shown in Fig. 138, the following rule should be used. Draw the half elevation as 
shown and through the flaring part of the ogee AB, draw the line ci, extending it 
until it intersects the center line CD at D. Take the stretchout from c to A and from i 
to B and place it as shown respectively from c to a and i to b. As either i or c repre- 
sents stationary points, take i and draw the semi-diameter i-E, and using E as center, 
draw the quarter section 1-6, which then divide as shown. Next develop the half pat- 
tern shown by similar reference letters, being careful to place twice the girth of the 
quarter section on similar arc i-i' in the pattern as shown. 




(E3X) 



FIG. 139. Applying the rules explained in connection with Figs. 135 to 138 in- 
clusive, obtain the flaring strips for the various moulds A~B-C shown in finial Fig. 139, 
each strip to be in one piece. 



TEXT BOOK ON PATTERN DRAFTING 



PATTERNS FOR FLARING STRIPS FOR CIRCULAR WORK, WHEN MADE 
BY HAND IN ARCS OF CIRCLES 

FIG. 140. When obtaining the flaring strips for window caps, circular pediments, 
etc., where the pattern is laid out in sections equal to 30 or 36 inches, the rule to be 




(E3X; 



Fig. 139. 



used is shown in Fig. 140, in which the elevation of a window cap is shown, with three 
different profiles on CA, as D, E, and F. From A, the center from which the arc is 
struck, draw the horizontal line AB. Assuming that the cove D is to be used, and 
requires "stretching," draw a line from a to b, and parallel to same tangent to the 




Fig. 140. 



curve at c draw the line cG, intersecting AB at G. Obtain the stretchout of the cove 
as given in the preceding problems and as shown by the solid line c. Then with G 
as center, the blank or pattern K is obtained. The amount of material required can 
be measured along the arc a°-a° and placed on the outer curve a in the pattern A', 



I04 



THE NEW YORK TRADE SCHOOL'S 



cutting as many pieces from metal as can be conveniently handled in "stretching." 
The quarter round E is developed in a similar manner and requires "raising." Draw 
a line from e to c^, and from the tangent point /, parallel to ed, the line hi is extended, 
until it intersects the center line AB at H. The girth ih is obtained in the usual man- 



SIDE 
ELEVATION 




(E4X) 



Fig. 141. 



ner and the pattern L secured, by measuring along a' , a distance equal to the outer 
curve a°-a° in elevation. The ogee m-n in F is laid off on r-s as shown. J is the center 
point from which to strike the pattern M, measuring along a" for the true girth of the 
arc. 



TEXT BOOK ON PATTERN DRAFTING 



105 



FIG. 141. Obtain the patterns for the various flaring strips required for the cir- 
cular base of a bay window, shown in Fig. 141 in which ABc is the side elevation and 
DE the plan view on the line A-B, the plan view being struck from the center F. 
After drawing the profile Ac, divide same into as many parts as there are seams, as 
shown by ad and be. Using the rule explained in the preceding problems, obtain G, 
the center from which draw the first flare 2-1-1'; also H from which to describe baa' 
and J the center for 4-3-3'. All center points fall upon the vertical hne drawn through 
F in plan. In laying out the approximate length for each pattern, the girth is taken 
from DE, LM and NO in plan, placing these lengths along the outer curves in A', Y 
and Z respectively, because the curved lines in plan represent the horizontal sections 
on similar lines in elevation, from which points the outer curves in pattern were ob- 
tained. 




Fig. 142. 



FIG. 142. In this figure ABCD represents portion of a panel having a curved head 
BC and the flaring strip for the curved mould is desired. FG represents the section of 
the panel, a part of which is placed on the center Hne drawn through E as shown by 
HJ. cd is then drawn parallel to ab, obtaining the center A^, from which fe is struck. 



io6 



THE NEW YORK TRADE SCHOOL'S 



PATTERN FOR FLARING STRIP FOR CIRCULAR WORK, WHEN MADE BY 

MACHINE 

FIG. 143. Shows the rule employed when obtaining the flaring strip for machine 
work. Let A BCD represent part elevation of a moulding running around the corner 
of a building as shown by EFGH in plan, the arc being struck from the center J 




Fig. 143. 



Above F, as shown, draw the profile BN and through the outer extreme points draw 
the line a-b; also through the inner extreme points draw dc. Bisect the distance da 
and cb and obtain e and /. Through / and e draw a line, extending it until the ver- 



TEXT BOOK ON PATTERN DRAFTING 107 

tical line drawn through the center point 7" in plan, is met at L. Then L becomes the 
center from which to strike the pattern. Starting at the lowest point of the moulding 
as i, obtain the stretchout of XB and place it as shown from i to /. Using L as center 
the part pattern jf'i'i is struck. The length can be measured along FG in plan and 
placed on //' in the pattern. It should be understood that in obtaining the length 
of FG, allowance must be made on //', because when passing the flaring strip through 
the dies in the machine, the ends have a tendency to round more than is called for. 
By having more material, the ends are cut as required, to make a miter joint with EF 
and GH in plan. 




Fig. 144. 



FIG. 144. Shows part elevation of a circular pediment by AB, C being the center 
point. D is the section of the mould and E the center for the pattern. Using the 
same rule given in previous problem, obtain the part pattern for the flaring strip. 



io8 



THE NEW YORK TRADE SCHOOL'S 



PATTERNS REQUIRED FOR INTERSECTION BETWEEN CONE AND CYLINDER 

PLACED VERTICALLY 

FIG. 145. Illustrates the principles for developing a vertical cylinder intersecting 
with a cone. This principle of obtaining a series of horizontal planes both in plan and 
elevation, can be applied to various problems, no matter what the profile of the pipe 
may be. First draw a plan view of the cone on its base line BC, and through the center 
e draw the diameter DE. Establish the location of the cylinder and with a as center 




Fig. 145. 



draw the circle 1-3-5-3. Divide the circle into equal spaces, as shown by the small 
figures i to 5 to i. Using e as center, with e-i, e-2, f-3, e-4 and c-5 as radii, draw 
circles as shown, intersecting the center line DE from i' to 5'. These circles then 
represent the plan views of horizontal planes, which are projected to the elevation, by 
erecting vertical line from i' to 5' until they intersect AC of the cone at i", 2", 3", 4" 



TEXT BOOK ON PATTERN DRAFTING 109 

and 5". From these intersections, horizontal lines are drawn, which are intersected by 
vertical lines, drawn from similar numbers in the profile of the cylinder in plan, result- 
ing in the intersections 1° to 5° in elevation. From 1° and 5° erect the vertical lines i°F 
and 5°G", which connect from F to G. Then i°-5° shows the miter line between the 
cylinder and cone. The pattern for the cylinder is obtained by Parallel Line Develop- 
ments as in Part One. The stretchout of a in plan is placed on HJ, and the pattern 
obtained as shown by HJP. As the pattern for obtaining the cone is similar in process 
to Fig. 112, we will only describe in Fig. 145 the method for obtaining the opening in 
the cone. With A as center and radii equal to A-5", A-4", A-t,", A-2" and A-i", de- 
scribe short arcs as shown. At pleasure draw the center line Ab. Then measuring, 
in each instance, from the center line DE in plan, take the various distances along the 
arcs to points 2, 3 and 4 and place them on similar arcs in the pattern, measuring 
on either side of the line Ab, thus obtaining points i" to 5". The shaded portion is the 
desired opening. Using the same size plan and elevation as in Fig. 145, obtain the 
necessary patterns, when the pipe is square, and placed diagonally as in Diagram A'; 
also when the pipe has semi-circular ends as in Diagram Y . In working out these prob- 
lems, the points a', e' in A' and a", e" in 1', should be placed over a and e in plan. 



PATTERNS REQUIRED FOR INTERSECTION BETWEEN CONE AND CYLIN- 
DER PLACED HORIZONTALLY 

FIG. 146. The principles in Fig. 145 are also applicable to the problem given in 
Fig. 146. Draw the elevation ABC and the plan view D. In its proper position in 
elevation draw the cylinder E-^°-^°-F, also its profile shown by H, which divide into 
equal spaces shown from i to 5 to i. Through these points draw horizontal lines, inter- 
secting AC as shown. From these intersections drop vertical lines intersecting ch in 
plan at 2-4, 1-5 and 2-4. Using a as center, draw the circles shown. On the center 
line be extended, place a tracing of H, as shown by H'-, giving the circle a quarter turn, 
bringing point i to the top. From these intersections horizontal lines are drawn, inter- 
secting circles having similar numbers, as shown by i' to 5' to i'. From these inter- 
sections vertical lines are erected, intersecting similar planes in elevation as shown 
from 1° to 5°. A line traced through these points gives the miter line between the 
cylinder and cone, which, however, is not necessary in developing the pattern for the 
cylinder, because the pattern could be obtained from the intersections in plan as well 
as from the elevation. The pattern for the cylinder is obtained in the usual manner. 
The opening in the cone is obtained in the manner explained in Fig. 145, being careful 
to take the distances along the arcs in plan in Fig. 146, measuring on either side of the 
center line be, and placing them on similar arcs in the pattern measuring on either side 



no THE NEW YORK TRADE SCHOOL'S 

of Ab'. Making drawing similar in size to that in Fig. 146, develop the patterns re- 
quired when the section of the pipe is square, as shown by the dotted lines inside of 




the circle H, also when the pipe is rectangular and is placed in a position shown by dotted 
lines outside of the circle. 



TEXT BOOK ON PATTERN DRAFTING 



PATTERNS REQUIRED FOR INTERSECTION BETWEEN CONE AND REC- 
TANGULAR PIPE PLACED HORIZONTALLY, TO ONE SIDE OF THE 
CENTER OF THE CONE 

FIG. 147, The principle in this problem, Fig. 147, does not differ from that given 
in Fig. 146, except in placing the horizontal pipes. In Fig. 146 the side view of the pipe 
is shown, while in Fig. 147 the end view is shown. We will assume that a rectangular 
pipe, 2-2''-5''-5, is to join a cone, so that the corner 2^ will meet the side of the cone 
as shown. Divide 2-''-5^ into any convenient number of parts and draw the horizontal 



rr-T^-^^ 




I (E3X) 



Fig. 147. 



planes through 2", 3^", 4" and s'', cutting the side of the cone as shown by 2-3-4-5. Draw 
the half plan on the various planes as shown, and complete the plan view of the pipe, 
cutting various planes in plan at 2' to 5' and 2" to 5". The pattern for the rectangular 
pipe is obtained in the usual manner, placing the stretchout of the rectangular pipe 
on DC, drawing the customary measuring lines, and intersecting same by lines drawn 
from similar numbers in plan. The radii from which the arcs n-o and st in the pattern 
are struck are obtained respectively from ^-5' and B-2' in plan, using r and u as center 
points in the pattern. For the opening in the cone, draw any radial line as ^-5°. With 



112 THE NEW YORK TRADE SCHOOL'S 

A as center and radii equal to A-2, A-^, A-4 and A-5, draw arcs as shown. Now meas- 
uring in each case from the line B-2' in plan, take the various distances along the var- 
ious arcs, to points z'-i", s'-3"> 4'-4" and s'-s" and place them on similar arcs in the 
pattern as shown by similar numbers, the shaded portion being the opening required. 
Applying the same principles as in Fig. 147, develop the patterns when the cylin- 
der a-b-c is tangent at a-b and c. Also obtain the patterns when the rectangular pipe 
a'b'c'd' is placed in the center of the cone, the two corners a' and b' touching the sides 
of the cone as shown. The patterns for the intersections between the pipe a'h'dd! and 
the cone could be obtained as in Fig. 146, but is introduced in Fig. 147 to show how 
it can be developed by placing the pipe in end view. It should be understood that the 
method shown in Fig. 146 can be used when the pipe comes centrally over the center 
line of the cone. But when the pipe intersects to one side of the center line. Fig. 147 
presents the operations more clearly. 



PATTERNS REQUIRED FOR INTERSECTION BETWEEN CYLINDER AND 
CONE AT OTHER THAN RIGHT ANGLES 

FIG. 148. The principles illustrated in Fig. 148 for obtaining the intersections be- 
tween a round pipe placed to one side of the cone at an angle in elevation, is appli- 
cable to any size cone or pipe, whether the pipe is round, square or elliptical and 
placed to one side or over the center of the cone. This problem presents an inter- 
esting study in projections and should be closely followed. Draw the center line AB, 
on either side of which place the half elevation of the cone as GCF . Using H as center 
draw the quarter plan 9-13. Divide this quarter circle into equal spaces, as shown by 
the small figures 9, 10, 11, 12 and 13, from which points draw radial lines to the center 
H. From these figures erect lines, cutting the base of the cone at 9'-io'-ii'-i2' and 
13', from which draw radial lines to the apex C. At the proper distance above F on 
the line FE, draw the elevation of the cylinder, also its section d, which divide into equal 
spaces as shown from i to 8, through which points parallel to the lines of the pipe draw 
the various planes, cutting the radial lines in elevation, also the center line AB and the 
base line GF as shown. It now becomes necessary to obtain in plan the different hori- 
zontal sections on the various planes in elevation. For example, where the plane \-e 
in elevation crosses the various radial lines, drop vertical lines to the plan intersecting 
similar numbered radial lines as shown, and take the horizontal distance from e to e' 
in elevation and place it as shown from H to i in plan. The curved line i-i in plan 
then represents the horizontal section on the plane \-c in elevation. Obtaining the 
other sections in the same manner, 2-8, 3-7, 4-6 and 5-5 in plan represent respectively 
the horizontal sections on the planes, /-2-8, 3-7, 4-6 and 5 in elevation. Having estab- 
lished these sections in plan, the next step is to locate the position where the side of the 



TEXT BOOK ON PATTERN DRAFTING 



113 



pipe 3 in d' in plan, is to meet the cone (in this case at 3') on the section 3-7, repre- 
senting the plane 3-7 in elevation. This point being established, take a tracing of 
d and place it in the position shown by d'. Through the various figures in d', draw 
horizontal lines cutting similar numbered sections, as shown by intersection i' to 8'. 
From these intersections vertical lines are erected, intersecting similar numbered planes 
in elevation as shown from i" to 8". For the pattern of the opening in the cone pro. 




Fig. 148. 



ceed as follows: Through the various intersections i' to 8' in plan, draw radial lines from 
the center H, intersecting the quarter circle 9-13 from i" to S"^ as shown. Also from 
the various intersections i" to 8" in elevation draw horizontal lines, cutting the side of 
the cone CG, from 1° to 8°. With C as center and radii equal to CG and CD, draw the 
arcs GJ and DL. Next take the various divisions in plan from 7^^ to 6'' to s'' to 8" 
to 4^^ to I "3" to 2^ and place them on the arc G'J, as shown by similar numbers, and 
draw lines to the apex C. Using C as center with radii equal to the various divisions 
between 4° and 8°, draw arcs, intersecting similar radial lines in the pattern, as shown 



114 



THE NEW YORK TRADE SCHOOL'S 



from i^ to 8^. Trace a curved line through these points, then will the shaded part 
be the desired opening. The pattern for the cylinder in X is obtained in the usual 
manner. A stretchout of d is placed on the line i-i in A', measuring hues erected and 
the various distances taken from the line a-b to points i" to 8", and placed on similar 
lines in A', as shown by similar numbers. 




c '^ I / 



HALF PLAN 



Fig. 149. 



FIG. 149. Using the principle in Fig. 148, obtain the patterns for the intersection 
between a square pipe and cone, the square pipe to be placed in the center of the 
cone, as shown in plan in Fig. 149. 2-2-5-5 is the profile of the square pipe, through 
which various planes are drawn as shown. The sections through the various planes 
are shown in plan, also the various points of intersections. The various patterns are 
also shown minus the reference letters. By carefully studying the diagram the student 
should have no difficulty in solving the problem. 



TEXT BOOK ON PATTERN DRAFTING 



IIS 



PATTERNS REQUIRED FOR CONE INTERSECTING CYLINDER AT AN ANGLE 
OF FORTY-FIVE DEGREES 

FIG. 150. The principles given in Fig. 150 for obtaining the intersection and 
developments between a cylinder and cone, can be applied to any problem, no matter 
what the angle may be; whether the vertical pipe is round, square or rectangular or 
whether the cone is placed in the center or to one side of the pipe. In this problem 
first draw the elevation of the round pipe BCDE, and below same the plan view, struck 




Fig. ISO. 



from the center a. In its proper position in elevation draw the cone A-f-f, extendmg 
the sides of the cone equally until a convenient base line 3'-?' is obtained. Below this 
line draw the profile E of the cone as shown, which divide into equal spaces i to 8. 
From these points, parallel to the center line of the cone, erect lines, cutting the base 
line of the cone from i' to 7', from which points radial lines are drawn to the apex A. 



ii6 



THE NEW YORK TRADE SCHOOL'S 



III this problem the center line of the cone in plan is to be placed to one side of the center 
line of the cylinder, the distance to be as is indicated from a to c. Therefore, through 
c parallel to ab, draw the line 7^', and from A in elevation drop a vertical line, inter- 
secting this line at A\ With w as center, draw the profile £', which is a duplicate of 
E, and change the position of the small figures as shown in E^. From the points i to 
8 in E^ draw horizontal lines, which intersect by vertical lines dropped from similar inter- 
sections on 3'- 7' in elevation, resulting in the points of intersections in plan shown 
from i" to 8". From these intersections draw lines to the apex ^4', crossing the plan 
of the cylinder from i to 8. From the intersections 1 to 8, vertical lines are erected, 
intersecting similar numbered radial lines in elevation as shown from 1° to 7°. A line 




Fig. 151. 



traced through these points as shown, gives the line of intersection. From the various 
intersections 1° to 7° at right angle to the axis of the cone, draw lines until they inter- 
sect the side of the cone from i to 8. For the pattern of the cone, use A as center, 
and with A-3' as radius, describe the arc 7-7. On this arc lay off the stretchout of the 
profile E. As the seam is desired at ^1-7° in elevation, then start at 7 on the arc 7-7, 



TEXT BOOK ON PATTERN DRAFTING 117 

as shown from 7 to 8 to i to 2, etc. From these figures draw radial lines to A, which 
intersect by arcs drawn from similar numbers on A-t,' with radii equal to the various 
divisions, resulting in the intersections 7=^ to 7"^ in the pattern. 7''4^7''/l is the desired 
pattern. The pattern for the opening in the cylinder is obtained by taking the stretch- 
out of the various intersections in plan and placing them on the line BC extended, as 
shown by similar numbers. Vertical lines are now drawn, and intersected by hori- 
zontal lines from similar numbers in the miter line in elevation, giving the inter- 
sections i^ to 8^ in the pattern. The shaded portion shows the desired opening. When 
enlarging this problem, the profiles E and £' should be divided into twelve spaces. 

FIG. 151. Using the principles in Fig. 150, solve in Fig. 151 the intersection 
between the cone B with the cylinder A, when the cone is placed in the center of the 
cylinder as shown in plan by B\ The profile of the cone is shown by a. Also obtain 
the patterns when the cone intersects a vertical square pipe, as shown by the dotted square 
in plan. D represents the plan view of a cone intersecting the side of a rectangular pipe 
placed diagonally in plan, a' representing the profile of the cone. Patterns for these 
two pieces are also to be developed. 



PATTERNS REQUIRED FOR INTERSECTION BETWEEN TAPERING SQUARE 
PIPE, AND VERTICAL SQUARE PIPE, PLACED DIAGONALLY 

FIG. 152. In this figure ABCD represents the plan view of a square pipe placed 
diagonally, intersected by a tapering pipe as shown in plan and elevation. The prin- 
ciples in this problem are similar to those in Fig. 150. E in Fig. 152 is the elevation 
of the square pipe; F, 1-2, 3-4, the elevation of the square tapering pipe, extended to 
an apex F, and a" the section on the base line a. From the intersections 1-2 and 3-4 
on the base line a, lines are projected into the plan, and the intersections i'-2' and 3'-4' 
obtained by taking the distances from a to 1-2 and a to 3-4 in elevation and placing 
them in plan as shown from a' to 1' and 2' and from a" to 3' and 4'. From these points 
radial lines are drawn to F\ cutting ABC of the square pipe from i" to 4". From these 
intersections lines are erected cutting similar radial lines in elevation as shown from 
1° to 4°. It will be noticed that the centers of the top and bottom of the tapering 
pipe intersect the corner of the vertical pipe in plan at B, shown in elevation by £' 
and B'. Before the pattern for the tapering pipe can be developed, the true radii 
must be found as follows: Equal in length and parallel to Fa, draw de. Take the dis- 
tance of the diagonal a'^i-and place it as shown from e to ay and draw a^'d. At right 
angle to Fa and from the various intersections i°-2°, 3°-4° and b draw lines intersecting 
a'''d at i°-2°, 3°-4° and b. With d as center and da^ as radius, draw the arc i-i, on 
which lay off the girth of a^ and draw radial lines to d as shown. Bisect 1-2 and 3-4 



ii8 



THE NEW YORK TRADE SCHOOL'S 



in the pattern and obtain B and B, which represents respectively the center Hnes of 
the upper and lower sides of the tapering pipe. With d as center and radii equal to 
d-b, d-i°2° and ti-3°4°, draw arcs intersecting similar radial lines in the pattern as 
shown. Take the distances of fB\ the center length of the upper side of the pipe and 
bB^, the center length of the lower side of the pipe, and place them in the pattern as 
shown respectively by fB^ and bB^. Connect the various points as shown by the heavy 
lines, which gives the desired pattern. The opening to be cut in the square pipe is 
shown shaded and is obtained by taking the girth of 4"-i"-B-2"-^" in plan, and plac- 



FATTERN FOR 

TAPERING 

SQUARE 

PIPE 




(E1X) 



Fig. 152. 



ing it on the lower line in elevation extended, as shown by similar numbers, from which 
vertical lines are erected and intersected by horizontal lines drawn from similar numbers 
in the miter line in elevation. Obtain the patterns required when the tapering pipe in 
Fig. 152 intersects the side of a rectangular pipe placed in the position in plan as shown 
by RSTC. The angle of the tapering pipe in elevation is to be similar as shown in the 
preceding problem. 



PATTERNS REQUIRED FOR INTERSECTION BETWEEN TWO CONES OF 

UNEQUAL DIAMETERS 

FIG. 153. The principles in this problem are similar to those given in Fig. 148. 
First draw the elevation of the cone as ABC in Fig. 153 and in its proper position below 



TEXT BOOK ON PATTERN DRAFTING 



119 



same place the plan view D. Divide the quarter plan 1-3 into equal spaces (in this 
case two) as shown by the figures 1-2-3, ^'^'^ draw radial lines to A' as shown. In 



HALF PATTERN / 

FOR //jl 

CONE / ' II \ 

/ / I 

■s?/ ; 




Fig. 153. 



enlarging this problem a larger number of divisions should be used in the quarter plan D 
and the half profile 4-6-8. From the intersections i, 2 and 3 in plan, erect lines cut- 



120 THE NEW YORK TRADE SCHOOL'S 

ting the base line CB at i'-2' and 3', from which radial lines are drawn to the apex A. 
In its proper position draw the elevation of the intersecting cone, as shown by F, 4°-8°. 
Extend each side equally any convenient distance, as shown by F4 and F8. Draw the 
line 4-8, bisect same, and obtain 6', which use as center and draw the semi-circle 4-6-8. 
Divide this into equal parts, shown from 4 to 8, from which points pei-pendicular to 
4-8, erect lines cutting 4-8 at 5'-6' and 7'. From these points draw radial lines to F, 
intersecting the radial lines in .the cone ABC as shown. The next step is to obtain the 
horizontal views of the cone ABC on the planes F-5', F-6' and F~j'. As the cones inter- 
sect each other center on center, then 4° and 8° in elevation will meet the center line 
in plan at 4^ and 8^. Where the plane F-f crosses the radial lines drawn from i' and 
2' and the base line at b, Hues are projected into the plan (not shown) until they 
intersect similar radial lines i and 2, also the plan of the base at b'. b'h' is then the 
horizontal section through the plane bit in elevation. In similar manner obtain the 
horizontal sections through the planes id and je, as shown in plan by i'd' and j'e' , the 
distances from A^ to e' and A^ to d' being obtained from e to f and d to c respectively in 
elevation. The next step is to find where the various planes in the intersecting cone 
i^4°8° cut the horizontal sections in plan. This is done by dropping lines from the 
points 4, 5', 6', 7' and 8 into the plan as shown, making the distances 5", 6" and 7", 
measuring from the center line F'£, equal to the distance 5, 6 and 7 in the half profile 
measuring from the line 4-8. Thus a line drawn from 5" to /■""' in plan cuts the section 
e'f at 5^ ; a line drawn from 6" cuts the section d'i' at 6^ and a line from 7" cuts the 
section b'h' at 7''. Now, from the intersections 4", 5^, 6"', 7^ and 8^ erect lines inter- 
secting similar radial lines in elevation at 4°, 5°, 6°, 7° and 8° as shown. From these 
intersections at right angle to the axis F-6' and A-t,' draw lines intersecting respec- 
tively the sides of the cones at F-S and A-B as shown by similar numbers. For the 
pattern of the cone (only one-half shown), use F as center and F-8 as radius and 
describe the arc 8-H, upon which place the girth of the half profile and draw radial 
lines to F, which intersect by arcs, drawn from F as center and radii equal to the divi- 
sions 4 to 8° on the line F-8, resulting in the intersections 4" to 8=^ in the half pattern. 
Through the various intersections 4^ to 8^ in plan, draw radial lines from the center A^, 
intersecting the circle at 4'^-8^, j'', 6^ and 5'. To get the opening to be cut in cone, 
use A as center and with AB as radius describe the arc BJ. Draw any line as A-4^&^ 
on either side of which place the stretchout of the spaces designated by T in the plan 
as shown on the arc B'J. Draw radial lines as shown, which intersect by arcs drawn 
from A as center with radii equal to the divisions between 4 and 8 on AB, resulting in 
points of intersections 4 to 8 in the pattern which is shown shaded. 

FIG. 154. Solve this problem in which two cones intersect, both axis being parallel, 
using the principles explained in Fig. 145. The outlines of the cones in Fig. 154 are 
first drawn as shown by ABC and CDE. The space between the intersections i'' and 4" 



TEXT BOOK ON PATTERN DRAFTING 121 

is divided into any convenient number of parts as shown by 2 and 3 and horizontal 
planes i-i, 2-2, 3-3 and 4-4 drawn through both cones. Show the horizontal sections 
in plan, through the planes i, 2, 3 and 4 in the cone ABC, as indicated from 1° to 4°, 




Fig. 154. 



using a as center. In similar manner show the sections through the planes in the cone 
CDE indicated in plan from i' to 4' struck from the center b. Where similar num- 
bered semi-circles intersect as at i", 2", 3^ and 4', lines are erected, intersecting similar 
planes in elevation as shown from i'' to 4''. Now, with D as center and with radii equal 
to Di, 2, 3 and 4'', describe arcs as shown. At pleasure draw DH. Obtain the girth 
in plan of 3' to 3'', 2' to 2^ and i' to i^ and place it on either side of the center 
line DH in the pattern, on arcs having similar numbers, thus obtaining the points of 
intersections i to 4, the heavy line showing the full pattern. For the opening in the 
cone draw the arcs as shown, and take any center line as AJ. Obtain the girth of 



122 THE NEW YORK TRADE SCHOOL'S 

c to 2^ and e to 3^ and place it on similar numbered arcs in the pattern, as shown 
from I to 4 on either side. Then will the shaded portion be the desired pattern. This 
same principle is applied no matter what size cones or fmstums are used. 



PART THREE— THE PRINCIPLES OF TRIANGULATION AS 
APPLIED TO DEVELOPMENTS OF IRREGULAR FORMS 

There are numerous irregular forms arising in sheet metal work, the patterns for 
which cannot be obtained either by parallel or by radial line developments. While 
possessing straight lines, these lines are not parallel, nor do they run to a common 
center. In working out patterns of this character, it becomes necessary, first of all, 
to divide the drawing representing the surface of the article into triangles. Then 
from the drawing, the true lengths of the various sides must be found, and the 
triangles constructed therefrom. This is the basis of Triangula tion. After the length 
of each side is known, it becomes a simple problem in geometry to construct the triangle, 
as illustrated in Fig. 155. In this figure, a-h, b'-c, and c'-a' are the given lengths 
from which to construct the triangle a-b-c. In the problems that follow, two methods 
of developing the pattern are shown, viz., with and without the aid of a plan. Under- 
standing both methods, the student will be in a position to apply, in practice, the one 
best suited to the work in hand. 



PATTERN FOR TRANSITION PIECE, RECTANGULAR TO SQUARE 

FIGS. 156 and 157. While irregular forms are largely curved surfaces, we can at the 
outset best illustrate development by triangulation by using a solid having plane sur- 
faces, as shown in Fig. 156, in which ABCD is the plan of the rectangular base, and EFHJ 
the plan of the square top, each side of which shows its true length. From the comers 
in the square plan draw lines to the comers in the rectangular plan, as shown. These 
lines then represent the bends which must be made in the article so as to form the 
transition piece, and also represents the bases of the triangles, which must be con- 
structed so as to find the true lengths of these lines. Knowing that the attitude is 
equal to LM in elevation the triangles are constructed as follows: Draw any hori- 
zontal line as aE and from a, erect the perpendicular a-b equal to the altitude of the 
article LM. As the square FEJH is placed directly in the center of the rectangle, 
then all that is necessary is to find the true lengths of EB and JB. Take these two 
distances and place them as shown from a to E and a to J , and draw the lines Jb and 
Eb, which represent respectively the true lengths of the lines JB and EB in plan. As- 



TEXT BOOK ON PATTERN DRAFTING 



12.1 



sume that the pattern is to be laid out in one piece, with a seam through NE in plan 
Take this distance NE and place it as shown from a to N, and draw a line from A' 
to b, which will be the true length on NE in plan. Having found the tme lengths of 
all the lines in plan, it only remains to place the various triangles in position in the 
pattern by using the same method as explained in connection with Fig. 155. Draw 




ELEVATION 
L P 




(E3 X) 



Fig. 155. 




any horizontal line as DC in the pattern in Fig. 156, equal to DC in plan. Now 
with radius equal to bE in the triangles, and D and C in the pattern as centers, de- 
scribe arcs intersecting each other at H. Draw lines from D to H and H to C. Then 
DHC is the pattern for DHC or AEB in the plan. With HJ in the plan as radius, 
and H in the pattern as center, describe the arc ;7, which intersect l:)y an arc, struck 
from C as center, and Jb in the triangles as radius. Draw a line from H to '7 to C in 
the pattern. Then HJC is the pattern for either HJC, JEB, EFA or FHD in the plan. 
With Jb as radius and J in the pattern as center, describe the arc B, which intersect 
by an arc struck from C as center and CB in plan as radius. Draw a line from J 
to B to C in the pattern, which is the pattern for the sides JBC and FAD in plan. 
JEB in the pattern is the reverse of JHC. Now, with radius equal to BN in plan, 
and B in the pattern as center, draw the arc N, which intersect by an arc struck from 



124 



THE NEW YORK TRADE SCHOOL'S 



E as center and hN in the triangles as radius. Draw the Unas E to N to B in the pat- 
tern which is the development of either ENB or EN A in plan. Take a tracing of 
ENCH in the pattern, and place it opposite the line HD and obtain the full pattern. 
This same pattern can be obtained by another method wherein the plan view is dis- 
pensed with. It is important to remember that the method which follows, can only 
be employed when both halves of the article to be developed are symmetrical, as shown 
in Fig. 157 by ^ and B, in which a-h and c-d are the center lines. If the article is not 
symmetrical as in plan C in Fig. 157, then the method just gone through must be em- 
ployed. 




Fig. 157. 



FIG. 158. To prove the second method and to show that the true lengths of the 
various lines will result ahke in both methods, Fig. 158 is given, in which OPRS is a 
reproduction of OPRS in Fig. 156. Take the half profiles of the top and bottom in 
plan and place them as shown, shaded by OEP and SDCR in Fig. 158. From E draw 
the vertical line Ea, and from a draw lines to 5 and R. Then will these lines in eleva- 
tion become the base lines, and the vertical heights in the profiles, the attitudes of the 
triangles, which will be constructed as follows: Take the distances PR and Ra and 
place them on any horizontal line as P^R'^ and R^a'. Make the distance a'E^ and 
R^C^ equal respectively to aE and RC and draw lines from £' to i?' and C^ to P^ repre- 
senting respectively the true lengths of aR and RP in elevation, and being equal to 
similar true lengths Eb and Jb in Fig. 156. To find the true length of the seam line 
a-b in Fig. 158 place it on a'-b' and make a'£' and b'O equal to aE and RC. Then 
will the distance E'C be the true length on a-b and equal in length to Nb in Fig. 156. 
Having found the true lengths in Fig. 158, the pattern is developed the same as in 
Fig. 156. In the problems that follow, the patterns are developed with and without 
the aid of the plan. Being familiar with both methods, the student, in practice, can 
apply either as best suits the work he has in hand. 



TEXT BOOK ON PATTERN DRAFTING 



125 



FIG. 159. Shows the plan and elevation of a transition piece from square to rec- 
tangle, both halves of which are not symmetrical when cut diagonally through 4-2, 
thereby making a plan view necessary in the development of the pattern. 1-2-3-4 
is the plan of the base, and 5-6-7-8 the plan of the top, a-b showing the vertical height 
of the article. 




(E 4 X); 




FIG. 160. Shows the plan and elevation of a transition from rectangular to square, 
both halves of which are symmetrical when cut through de. i to 4 is the plan of the base, 
and 5 to 8 the plan of the top. In this case no plan view is necessary in laying out 




126 



THE NEW YORK TRADE SCHOOL'S 



the pattern. Simply take the half profiles of a and b in plan, and place them in their 
proper positions in elevation as shown by the shaded parts a' and b', and develop the 
half pattern as explained in connection with Fig. 158. 



PATTERN FOR OBLIQUE CONE 

FIG. 161. Shows the manner of developing the pattern for an oblique or scalene 
cone. The student should understand that any plane in a scalene cone drawn parallel 
to its base as DE in elevation, will have a similar shape as the base differing only in 
size. This applies to all articles, the bases of which can be inscribed in a circle. Let 
ABC represent the elevation of a scalene cone. Draw the plan view on the line AB, 
struck from the center a and through a draw the horizontal line a-C\ which intersect 
at C by a line drawn from C in elevation at right angle to AB. Divide the circle a 




(E4X) 



into equal parts shown from i to 5 to i, and draw lines to the apex C\ (In enlarging 
this problem divide the circle a into twelve parts. With C as center and radii 
equal to C4, 3 and 2 draw arcs intersecting the center line iC at 2', 3' and 4', from 



TEXT BOOK ON PATTERN DRAFTING 



127 



which points erect Hnes intersecting the base line AB at 2", 3" and 4". Lines are drawn 
to the apex C, but are not necessary in practice. Using C as center, with radii equal 
to Ci", C2" , Ct,", C4" and C5", draw arcs as shown. Draw any line from the arc made 
from radius 5", as 5°C Now set the dividers equal to the spaces contained in the plan 
a, and starting from 5° step from one arc to another, as shown by 4°, 3°, 2° and 1°, 
after which complete the opposite half to s''. A line traced through these points as 
shown by C"5''i°5°C will be the desired pattern. As previously stated, the section of 
any line or plane drawn parallel to the base will have similar section differing only in 
size; therefore to prove this, draw at pleasure any line as DE, and from a in plan erect 
a vertical line, intersecting AB at a' , from which draw a line to the apex C, cutting the 
line DE at .Y. From .Y drop a vertical line, intersecting similar center line in plan at b. 
Now, with b as center and radius equal to either XE or XD, draw the circle shown, 
which will be tangent to the lines 3-C"^ DEB A represents a frustum of an oblique cone, 
and to obtain the upper cut DE on the pattern, use C as center, and with radii equal 
to the various divisions on DE, draw arcs intersecting similar radial lines in the pattern, 
thus obtaining the cut S'l's". 




Fig. 162. 



FIGS. 162 and 163. The preceding rule can be used whether the pipes are round 
or square, also when the ends are semi-circles, as shown in Fig. 163. In large work, 
when the center point C in Fig. 161 cannot be used in describing the patterns, a 
different method is employed, which will be explained later. The method in Fig. 161 



128 



THE NEW YORK TRADE SCHOOL'S 



is also employed for developing reducing offsets, as will be seen in the problem that follows. 
Obtain the pattern for a reducing offset, having outlet equal to A in Fig. 162 and 
an inlet equal to B: the distance from center to center being equal to AB and the 
vertical height equal to ab. Construct from the plan the elevation aEDC, and extend 
the lines until the apex is obtained. Obtain the apex F' in plan and proceed to develop 
the pattern as explained in Fig. 161. Referring again to Fig. 162, make a new drawing 
and in a like manner obtain the pattern for a reducing square pipe. The sizes of H 



HALF PATTERN 





(E3X) 



PLAN 

Fig. 164. 



and J are as shown. The altitude is to be equal to a-b. The true lengths of the comers 
must be obtained as partly indicated by a' and b'. In Fig. 163 the pattern is to be ob- 
tained for the transition piece, the sides of the base being flat, with semi-circular ends, 
and the top round. In this problem a~b and a'b in plan, represent each one-half of 
a scalene cone, whose apex in elevation and plan are shown respectively by B and B\ 
When the pattern for a-b is developed, it is only necessary to add the flat sides c-d 
and c'd' to it. This flat part appears in elevation by A, but does not show its true surface. 



TEXT BOOK ON PATTERN DRAFTING 



129 



PATTERN FOR RAISED COVER 

FIG. 164. The principle given in the preceding problem is applicable to the raised 
cover development in Fig. 164, where 1-4-1-4' is the plan view and 4-A-4' the eleva- 
tion, the semi-circles in plan being struck from a and h. As the four quarters in plan 
are symmetrical, then divide the quarter plan as shown from i to 4, being careful to 
have more divisions when enlarging the problem. Draw lines to the apex A' in plan 
and let i-A'-i represent the seam line of the cover. Take the various distances in 
plan as A'l, A'2 and A'3, and place them in elevation from X to i, 2 and 3 and draw lines 
to A. These lines then represent the true lengths of similar numbered Hnes in plan. 
For the half pattern use A as center and with radii equal to Ai, A2, /1 3 and A 4 draw 
arcs as shown. From the arc made from point 4 draw the line 4~A in the pattern. 
Next set the di\nders equal to the various divisions in the quarter plan 4-1 and lay the 
spaces off" on corresponding arcs in the pattern, on either side of the line 4- A. A line 
traced through the various intersections shown by yl-i-4-i-.4 is the half pattern, with 
seam on i-i in plan. 




USE SAME 

SIZE PLAN 

FOR SIX 

POINTED STAR 




(E4X) 



Fig. 165. 

FIG. 165. By the preceding method solve the two problems given in Fig. 165, the 
altitude in elevation of both to be equal to B. A is the plan view of the one with 
rounded comers, struck from the centers a-b-c and d, and plan .4' is a rosette having 
eight flutes. Separate drawings are to be made for each problem. 

FIG. 166. The principles in Fig. 165 also apply to Fig. 166, which shows a plan 
view of a five-pointed star, the height of which is equal to ii-a in elevation. As a-b 



I30 THE NEW YORK TRADE SCHOOL'S 

in plan is placed on a horizontal line, a-b in elevation will show its true length on a~b 
in plan. In plan c-b also shows its true length. The true length of a-c in plan is ob- 
tained by taking the length of a-c or a-c' in plan, and placing this distance from u 
to c in elevation, and drawing a line from c to o the length desired. For the pattern, 
make a-b in the pattern equal to a-b in the elevation ; with be in plan as radius and b 
in pattern as center, draw the circle c-c, which is intersected by the arc c-c, struck from 
a as center and a-c in elevation as radius, then a-c-b-c-a is the pattern for one point. 
If a section were required on the line c-c° in plan, at right angle to a-b in elevation, 
then extend c-c° until it intersects the base line in elevation at e, from which point at 
right angle to a-b draw ei. Place this distance ei from e to i in plan. The shaded 
section is the true profile desired, and the distance of either ic or ic° will equal ic in 
the pattern. In similar manner develop the pattern for a six-pointed star, making 
a separate drawing. 



PATTERN FOR TRANSITION PIECE, IN WHICH BOTH HALVES ARE SYM- 
METRICAL AND NO PLAN IS REQUIRED 

FIG. 167. In developing this problem the principles made use of are those given 
in connection with Figs. 158 and 160, and as illustrated in Fig. 167, which shows a tran- 
sition piece, both sides being symmetrical as indicated in plan. When the student be- 
comes familiar with this method of development, no plan view is necessary, but is here 
shown so as to make clear the various steps taken. In this method, when omitting 
the plan, the elevation of the article to be developed must always be drawn at a right 
angle to the line which divides the article into two symmetrical parts, as per line a-b in plan. 
Let 1-5-6-9 be the elevation of the transition piece. Place the half profile of the round 
top on 1-5, as shown by 1-3-5, and the half profile of the rectangular base on 6-9, 
as shown by 6-7-8-g. Divide the semi-circle into equal spaces as shown (being careful 
to use double the number of divisions in enlarging this problem) and from the points 
2 to 4 drop vertical lines intersecting 1-5 at 2'-^' and 4'. From points 2' and 3' draw 
lines to 9 and from 3' and 4' draw lines to 6. These lines will then represent the base 
lines of the sections to be constructed, the altitudes of which will be equal to the 
various heights in the half profiles. These true lengths are shown in A and B and are 
drawn as follows: Take the distances in elevation of 9-1, 9-2' and 9-3' and place them 
on the horizontal line in yl, as shown by similar numbers. At right angle to the hori- 
zontal line in A, erect the lines 9-8, 2'-2 and 3,'-^,, equal respectively to similar numbers 
in the half profiles in elevation. Then 8-1, 8-2 and 8-3 in A represent the true lengths 
of similar lines in elevation. The true lengths shown in B are obtained in a similar 
manner from measurements in elevation. In this case two diagrams A and B are shown. 



TEXT BOOK ON PATTERN DRAFTING 



131 



but in practice one diagram is sufficient on which all the true lengths can be found. 
Assuming that the pattern is to be developed in two pieces, with seams at d and e in 
plan, draw any line 1-9 in D equal to 1-9 in elevation. With 9-8 in the half profile as 
radius, and 9 in Z? as center, draw the arc 8, which is intersected by an arc, struck 
from I as center and 1-8 in .4 as radius. Draw a line from i to 8 to 9 in Z). Now with 
8 as center and radius equal to 8-2, and 8-3 in A, draw the arcs 2 and 3 in D. Set 
the dividers equal to 1-2 and 2-3 in the half profile, and starting from i in D, lay off 
this distance on arcs 2 and 3, and draw a line from 3 to 8. With 8-7 in the half profile 
as radius, and 8 in Z) as center, draw the arc 7, which intersect by an arc struck from 






(E 3X) 



TRUE LENGTHS 




HALF PATTERN 



Fig. 167. 



3 as center, and 3-7 in B as radius. Draw a line from 3 to 7 to 8 in D. Now with 
radius equal to 7-4 and 7-5 in B and 7 in D as center, describe the arcs 4 and 5. Set 
the dividers equal to the spaces 3-4 and 4-5 in the half profile in elevation, and 
starting from 3 in the pattern D, step to arc 4, then to 5 and draw a line from 5 to 7. 
With radius equal to 6-7 in the half profile in elevation, and 7 in D as center, draw 
the arc 6, which intersect by an arc struck from 5 as center, with radius equal to 5-6 
in elevation. Draw a line from 3 to 6 to 7 in D. Then 5-6-9-1 is the half pattern. 
No matter what the profiles of the ends may be, the above principle is used, it being 



132 



THE NEW YORK TRADE SCHOOL'S 



immaterial whether the hnes 1-5 and 6-9 run parallel to each other or not, as will be 
explained in the following problems. In the sixteen problems that follow, the profiles 
should be divided into twice the number of spaces shown in some of the problems, for 
the reason that the more spaces that are used, the more accurate is the pattern. The 
plan views will be shown in the sixteen problems that follow, but that view is not 
necessary in the development of the patterns; they indicate only that both halves of 
the article are symmetrical. In developing these patterns for these sixteen tran- 
sition pieces, only one-half the pattern is required, with seams through a-b, excepting 
Figs. 182 and 183, in which the full patterns are required. In Fig. 167 a transition 
was developed, in which one side was vertical. 

FIG. 168. In this figure a transition piece is to be developed where the upper pipe 
comes directly in the center of the rectangular base. .4 shows the elevation, B the 
half profile of the top and C the half profile of the base. 



(tSX) b 
Fic. 168 



, PLAN 






( B ^ 




^ 


/ 


ELEVATION 


\ 


: C /': 


\ 


/ : 


\ 


/ ; 


r 


^\^ 



'tE4X) 



FIG. 169. Develop the half pattern of the transition piece, whose base is rectan- 
gular and top round, placed to one side. It will be noticed that the elevation A is 
drawn at a right angle to the line a-b, which divides the article into two symmetrical 
parts. On the top of the elevation .4 in Fig. 169 the half section B is placed, and on 
the bottom, the half section or profile C, the true lengths and pattern being obtained 
as in Fig. 167. 

FIGS. 170 and 171. In Fig. 161 we explained how the pattern for an oblique cone 
was developed when the center point could be used. Figs. 170 and 171 show how ;i 
transition piece forming a frustum of an oblique cone is developed, when the work is 



TEXT BOOK ON PATTERN DRAFTING 



133 



large and no center can be used. The principles are exactly the same as in Fig. 167. 
In Fig. 1 70 is shown a transition piece, both ends of which are round, one side being 
vertical. .4 shows the elevation with both half profiles in position as B and C. The 
method of drawing the base lines is the same as given in Fig. 171, in which the top 
opening is placed outside of the lower one. The elevation A and the half sections or 
profiles being drawn, B and C are both divided into the same number of spaces, and 
from these points lines are drawn at right angles to their respective base lines as shown. 
Alternate solid and dotted lines are then drawn as shown, connecting opposite points, 
after which the true lengths and pattern are obtained as before. 





PLAN '^' ( E •* X) 

Fig. 172. 



(E4X) 



■ FIG. 172. Shows a transition piece, having a top that is round and base that is 
oblong with semi-circular ends. The half profiles B and C are placed on the elevation 
as shown, and each of the quarter circles in C, divided into one-half the number of 
spaces contained in B. Then solid and dotted lines are connected as shown. 

FIG. 173. Is a problem where the oblong top is similar and connected to a round 
base placed outside the top. The half profiles B and C are placed on A as shown, and 
divided as shown and explained in the previous problem. 

FIG. 174. Shows a transition piece, the bottom of which is oblong, placed at right 
angles to the center line a-h, the top being a rectangle. Note that the semi-circle 
in C is equally divided, and lines carried to the base Hne 6'- 10', thence to the corners 
2' and 3'. 2'-io' and b'-T,' in A show their true lengths, but the others must be found 
as previously explained. 



134 



THE NEW YORK TRADE SCHOOL'S 



FIG. 175. Shows a transition piece where two oblong pipes, with semi-circular 
ends, cross each other. The elevation A is drawn and the half profiles placed in the 
position shown. Be sure to divide the quarter circles in B and C into the same 
number of parts as shown, and connect solid and dotted lines as there indicated. 
Whether the profiles are oblong or elHptical the rules remain the same. 




(1- 




(E4X) 



Fig. 174. 



Fig. 176. 



FIG. 176. Shows a similar problem, the upper opening being placed away from the 
lower. The half profiles B and C are joined to ^4 as shown, and spaced in a manner 
similar to Fig. 175. 

FIG. 177. Shows a transition piece where the top plane aV does not run parallel 
with the bottom. In this case, as in the others, no plan view is required; for knowing 
that both halves on either side of a-b are symmetrical, the half profiles are placed on 
either end of A as shown by B and C, both of which are divided into the same number 
of spaces and the solid and dotted lines drawn as before. A horizontal view on 
a'-c' would show an elliptical figure in plan. Although this view is not necessary, the 
method of obtaining it will be described, a'b'c' in plan is equal to a'tV in elevation, 
and a"c" in plan is obtained by projecting ^'ertical lines from a'-c' in elevation as shown. 



TEXT BOOK ON PATTERN DRAFTING 



135 



FIG. 178. In this figure A shows the side view of a transition piece, whose openings 
run at right angles to each other. A front and plan view are shown to make the 
drawing more clear, but are not necessary when developing the half pattern. The 
method of spacing the half profiles B and C are clearly shown. 

FIG. 179. In this figure the inlet and outlet are both rectangles, otherwise the 
problem is similar to Fig. 178. In this problem no front or plan views are required, 
the half profiles B and C being placed on .4 as shown. As the half profiles have no 
curved surfaces, the only line required is that from 3' to 7'. The true lengths and half 
pattern are obtained in precisely the same manner as in former problems. If, in this 
problem, one end was square and the other round, the method of drawing the solid 
and dotted lines would be the same as in Fig. 167. 





FRONT ELEVATION 

NOT NECESSARY 

IN DEVELOPING 

THE PATTERN 



FIG. 180. In this figure 1-5-6-10 is the elevation of a tapering collar, to fit over 
a pitched roof, indicated by DE. The lower part of the collar along the line DE is to 
have an equal horizontal projection all around the upper opening 1-5, as indicated by 
hi and de. The full horizontal diameter is equal to rs, which bisect and obtain t. From 
t drop a vertical line, cutting DE at 11, and from ;/ draw the perpendicular 11-8 equal 
to rt or ts. Now, through h-8-e draw the curve shown, which in this case has been 
struck from iv. The half profiles B and C are spaced as shown. 



136 THE NEW YORK TRADE SCHOOL'S 

FIG. 181. Shows a similar collar having a round top and a square base, when 
viewed on a horizontal line. In other words the projection on either side of the 
round top is to be equal, as shown by d-&' and e-j'. The full distance being equal 
to hi, take one-half of this and place it at a right angle to S'-y', as shown by 8'-8 
and y'-j. The half profiles B and C are then placed on A as shown. 



SIDE 
ELEVATION 



7U 




FRONT ELEVATION 

NOT NECESSARY 

IN DEVELOPINO 

THE PATTERN 



( E 4 X) 




(E4X) 



Fig. 179. 



Fig. 180. 



FIG. 182. In this figure A shows the side view of a tank hood, the section of 
which on the base line is equal to part of a circle, as shown in plan by cfe, and the 
section on the vertical line in A being shown in front view by c'ie'. It should be under- 
stood that no plan or front view is necessary when developing the pattern. All that 
is required is the half profile def placed at C, and the half profile (/d'i placed at B. 
Both profiles are divided into the same number of parts as shown, and the true lengths 
obtained and full pattern developed. If the height d'i in front view were not given, 
the pattern could be obtained by parallel lines as shown in Figs. 39 and 40 in Part One. 

FIG. 183. Illustrates the development of the full pattern for a forge hood. 1-5- 
6-8°- 10 is the side view of the hood, B the half profile of the upper opening, C the half 
profile of the forge, to which it connects as shown in plan by Iiij, and D the section 
which must be found by drawing a line at a right angle to 10-8°, from the point 8° to 8', 
equal in length to 8°-8, and then at pleasure drawing the curve 8'-io. In spacing 



TEXT BOOK ON PATTERN DRAFTING 137 

the profiles in any article in which three profiles are given, the following rule should 
always be followed, viz.: To divide the profile B into as many divisions as there are 
spaces in the profiles C and D. In enlarging this problem more divisions should be 
used than here shown. There is no limit to the various transition pieces whicli can be 
developed by the method of omitting the plan, when both halves are symmetrical, 
/.h \i 




(E4X) 



3 1 SIDE VIEW 

A 




tE5>) 



Fig. 181. 



Fig. 182. 




138 



THE NEW YORK TRADE SCHOOL'S 



PATTERN FOR A TRANSITION PIECE, IN WHICH BOTH HALVES ARE 
NOT SYMMETRICAL, AND A PLAN IS REQUIRED 

FIG. 184. Shows a transition piece. The base is rectangular and top round, and 
the halves are not symmetrical. In this case the true lengths are obtained by using 
the lines in plan as the base lines, and the vertical height be as the altitude. ABCD 
is the plan of the base, and 1-3-5-7 the plan of the top, struck from the center a. 
EFH'J is the elevation. In diagram L the true lengths appear for those lines shown 
in plan in .4-1-3. I" diagram M, N and the true lengths are shown respectively for 




Fig. 



the lines in plan in 5-3-5, C-5-7 and D-y-i. For example: the distances of Ai, A2 
and A3 in plan are placed on the line JH extended, as shown by A°i, A°2 and vl°3, 
and slanting lines drawn to A also shown, A°A being the altitude equal to a-b. As- 
suming that the pattern is desired in one piece with a seam along 5^ in plan, start by 
taking AD in plan and placing it on AD in pattern. Using A and D as centers, with 
radii equal to A-i in L and Di in 0, draw arcs intersecting each other at i in the pattern. 
Proceed to develop the pattern as shown in Fig. 167, following the reference figures 



TEXT BOOK ON PATTERN DRAFTING 



139 



and letters in Fig. 184, the lengths 5<? in the pattern being obtained from FH in the 
elevation. By comparing measurements between the plan, the true lengths and the 
pattern, no trouble should be experienced in developing the pattern by following refer- 
ence letters and figures. 

FIG. 185. Develop the full pattern for the transition piece shown in Fig. 185, with 
the seam on Ai in plan, the vertical height being indicated by a-b in elevation. The 
method of obtaining the true lengths and pattern is similar to that shown in Fig. 184, 
but care must be taken to divide the plan view as indicated in Fig. 185. Note how 
the sides of the rectangular base terminate in the four parts of the circle ; that is, 
AD to I, DC to 7, CB to 5, and BA to 3; then each of the quarter circles to corre- 
sponding comers in the base. In plan, c is the center of the circle. 



ELEVATION 





Fic. 186. 



FIG. 186. Is the plan and elevation of a transition piece oval to rectangle. The 
vertical height is equal to a-b and the semi-circles in plan are stiuck from c and d. 
The flat surface i-io connects to A-D, 5-6 to B-C, CD to 8, and BA to 3. The quarter 
circles 1-3 connect to .^4, 3-5 to B, 6-8 to C, and 8-10 to D. Develop 
the full pattern with a seam on i-A. 

FIG. 187. Develop the full pattern for the transition piece shown in Fig. 187, with 
a seam on i-i'. The flat sides in the oval section I'-i" run to i, and s'-s" run to 5. 
The semi-circles in top and bottom are both divided into similar spaces as shown and 



140 



THE NEW YORK TRADE SCHOOL'S 



connected by solid and dotted lines. Thus, solid lines are drawn from 6 to 6', 7 to 7', 
8 to 8', etc., and then the dotted lines connected the shortest way, as from 6 to 5", 
7 to 6', etc. a and b are the centers of the semi-circles, e the center of the circle, and 
cd the vertical height of the transition. In obtaining the true lengths, make a separate 
diagram for the solid lines, and a separate one for the dotted lines. 




(E4X) 



Fig. 187. 



PATTERN FOR TRANSITION ELBOW, ROUND TO OBLONG, IN WHICH 
THE EXTERIOR ANGLE IS A RIGHT ANGLE 

FIG. 188. Shows the method employed, when transition elbows are to be developed 
in two pieces, whether the exterior angle is a right angle or otherwise, and the upper 
arm a parallel pipe, and the taper taking place on the inside angle of the lower arm. 
In this case there is a transition elbow having an oblong inlet with semi-circular ends 
and the outlet a circle. A represents the elevation of the elbow, B the profile of the 
top arm and C the profile of the opening of the lower arm. The miter line 1-5 can 
be the bisection of the exterior angle, or may be established at pleasure. The profile 
B is divided into equal spaces (have more spaces in enlarging the problem) and lines 



TEXT BOOK ON PATTERN DRAFTING 



141 



carried parallel to the upper arm, until they intersect the miter line 1-5. The pattern 
for the upper arm is shown by D and is obtained as explained in Part One on Elbow 
Patterns. The pattern for the lower arm forms a transition piece and is developed 
by triangulation as follows : Divide the semi-circles in the profile C into the same number 
of spaces as shown in the semi-circles in B. Erect vertical lines from C, intersecting 
the base of A as shown. Draw solid and dotted lines in A as shown and obtain the 



3^ 3' ^ 8° 9 



TRUE LENGTHS OF 
SOLID LINES 




true lengths of the solid lines in A, by taking those distances and placing them on 
the horizontal line in E, as shown by similar numbers, and from these numbers erect 
vertical lines, making them equal in height to similar numbers in B and C, measuring 
from the Hne 1-5 and 6-1 1 respectively. For example: 3-8 in A is placed on the hori- 
zontal line as 3-8 in E, the vertical heights t,-t,° and 8-8° being equal to the heights 



142 



THE NEW YORK TRADE SCHOOL'S 



measured from the line 1-5 to the point 3 in B, and from the hne 6-1 1 to the point 
8 in 6" respectively. 3°8° in E then shows the true length of the line 3-8 m A. In 
this manner all of the true lengths of the solid lines in E and dotted lines in F are ob- 
tained. The pattern for one-half the lower arm is shown developed and is obtained 
as follows: Take the distance 5-1 1 in A, which shows its true length, and place it as 
shown by 11-5' in H. Using ii-io in C as radius, and 11 in // as center, describe the 
arc 10, which intersect by an arc struck from 5' as center, and 5-10 in F as radius. 
Now, with 5'-4' in the pattern D as radius, and 5' in H as center, describe the arc 4', 
which intersect by an arc struck from 10 as center and 10-4 in E as radius. Proceed 
in this manner, using alternately as radius, first the divisions in the profile C, then the 
true length in F\ the divisions in the miter cut in D, then the true lengths in E, the 
distance i'-6 in H being obtained from 1-6 in A. 

FIG. 189. Apply the same principles given in Fig. 188 to Fig. 189, in which an 
elbow is shown round to square. A is the ele\'ation of the upper arm, and D its profile. 
B is the elevation of the lower arm, and C its profile on I'-s'. The pattern for A is laid 
off on ed. Solid and dotted lines are drawn in B as shown. The true lengths of the 
lines are obtained by using these lines as bases, and the heights in the semi-profiles 
D and C as altitudes, measuring from the lines a-b in D, and 1-5 in C respectively. 



I 

PROFILE 



(E 4X) 





Fig. 189. 



Fig. 190. 



FIG. 190. Develop the patterns for an elbow rectangle to square, having an exterior 
angle of 45°. The pattern for A is laid off on ef. D is the profile for the opening in 
.4, and C for the opening m B. A dotted line is drawn from 1' to 4'. The altitudes 



TEXT BOOK ON PATTERN DRAFTING 



143 



for obtaining the true lengths are obtained from the semi-profiles D and C, with bases 
equal to the lines in B. Note the reference numbers in the profiles. 

FIG. 191. Shows an elbow to be developed, both profiles of which, D and C, are 
equal but cross each other at right angles when viewed in plan. Note how the profiles 
are spaced and the dotted and solid lines drawn. The pattern for A is Taid off on cd, 
the true lengths obtained by using the lines in B as base lines, and the heights in the 
semi-profiles D and C as altitudes. The pattern for B is obtained in a similar manner 
to that used for obtaining H in Fig. 188. 




Fig. 191. 



PATTERN FOR TRANSITION ELBOW, ROUND TO OBLONG, IN WHICH 
BOTH EXTERIOR AND INTERIOR ANGLES TAPER 



FIG. 192. The principles given in connection with Fig. 192 can be applied to any 
tapering elbow, no matter what profile either end may have. Let ABCDEF be the 
elevation of a tapering elbow with section on 'DC as shown by G, and section on AF 
as shown by H. Since the width of one-half of H is less than one-half of G, the width 
at ;' on EB should be a medium between the two. Therefore, take the distance of 
i~e in H and place it from / to e' in G. Bisect e'-j and obtain 0. Then i-o is the dis- 
tance to be placed in the center and at a right angle to EB, as shown by i'-o' . Through 



144 



THE NEW YORK TRADE SCHOOL'S 



Eo'B draw the semi-elliptical figure shown which will be the true half section on EB. 
Knowing the true profiles or sections on AF, EB and DC, proceed to obtain the pat- 
tern in precisely the same manner as explained in connection with the transition piece 
in Fig. 167 and as solved in the problems Fig. 168 to Fig. 181 inclusive. X in Fig. 




(E4X) 



Fig. 192 



192 is a reproduction of ABEF, J the half profile of H, and L a reproduction of Bo'E 
in elevation. The sections J and L are divided as shown. Y is a reproduction of 
BEDC, U being a reproduction of L in A', and M one-half of the section G. The 
semi-circle in M is divided into as many spaces as contained in L', and solid and dotted 
lines drawn in the usual manner. 

FIG. 193. Develop the patterns for a tapering two-pieced elbow from round to 
rectangular, as shown in Fig. 193. The opening of A is shown by C, while the opening 



TEXT BOOK ON PATTERN DRAFTING 



145 



of B is shown by D. The distance ac in C is set off from a' to c' in D, and the distance 
h to c' bisected, thus obtaining i. This distance a'-i is set off at a right angle to 
a°-a°, as shown from a° to j° on both sides. Reproductions of A and B with their 
respective profiles are then drawn as explained in Fig. 192. 



; c 

PROFILE ' 




(E4X) 



Fig. 193. 



PATTERN FOR THREE-PIECED TRANSITION PIECE 



FIG. 194. The problem given in Fig. 194 does not differ from that given in Fig. 
188 as far as the principles are concerned. Fig. 194 shows the elevation of a three- 
pieced transition piece round to round. .4 is the upper arm with profile as shown 
by B, and C the lower arm, the profile of which is D, both being parallel pipes. Both 
profiles are divided into similar number of spaces as shown, and lines carried parallel 
to the line of the pipes A and C, until they intersect the miter lines 6-10 and 1-5 
respectively. The patterns for A and C are obtained by parallel Hues as shown. SoHd 
and dotted Hnes are now drawn in H and represent the base lines of sections which are 
to be constructed, with altitudes equal to the various distances in the semi-profiles 
B and D, each having similar numbers; or in exactly the same manner as explained 
in connection with diagrams E and F in Fig. 188. After the true lengths have been 
obtained for Fig. 194, the pattern for H is developed, by using the true lengths 



146 



THE NEW YORK TRADE SCHOOL'S 



which are to be found, and the various distances in the miter cuts F and E, or in 
exactly the same manner as explained in connection with developing the pattern H in 
Fig. 188. The diagram of sections and pattern for H in Fig. 194 are not shown, but 
are to be drawn when enlarging this problem. 



PATTERN FOR A 




Fig. 194. 



FIG. 195. Develop the patterns for a transition boot, oblong to scjuare, illustrated 
in Fig. 195. A IS the upper arm, having profile B, and C the lower arm, having profile 
D. The patterns for both of these arms are laid ofif on c-d and a-h respectively. The 
profiles are spaced and numbered as shown, and the true lengths of E and its pattern 
are obtained as in Fig. 194. A line should be drawn from i to 5 in elevation in Fig. 195. 

FIG. 196. Develop the patterns for a three-pieced elbow round to square. The 
]:)attern for the square pipe is laid off on c-d and for the round pipe on a~b. The method 
of spacing the profile is shown. 



TEXT BOOK ON PATTERN DRAFTING 



147 





(E4X) 



FIG. 197. In this figure develop patterns for an elbow oblong to round. It makes 
no difference whether the transition piece is shaped as shown in Fig. 194 or as shown 
in Fig. 197, the same methods apply in each case. 




148 



THE NEW YORK TRADE SCHOOL'S 



PATTERN FOR TWO-PIECED TAPERING FORK 

FIG. 198. Shows the principle that can be used in developing a two-pieced tapering 
fork, in which the diameters of both A and B are equal. Draw the elevation as shown, 
and at right angle to the various openings place the profiles in position. As hk repre- 
sents the seam line between the two forks, a true section must be found on this line 
as follows : As the horizontal distance through k is equal to b-c in the profile, then take 
one-half this distance as a-c, and place it at right angle to h-k, as shown by k-i, and 
at pleasure draw any desired curve as t-h. The shaded part h-k-i then becomes the 
true half section on h~k and is used when obtaining the pattern by triangulation, in 
a manner as shown in Fig. 183, and as will be explained in connection with Fig. 198. 



.1 ^13 ~i' J 




true lengths of solid 
lines in c 
Fig. 198. 



PATTERN FOR 
ONE PRONG 



To avoid a confusion of lines, C is a reproduction of B. Take the half shaded profiles 
e~f, h-k-i and a-c-d in B and place them in C, as shown respectively by 1-3-5, io-8°- 
8' and 8°-8-6. Divide the profiles into equal spaces as shown, being careful to divide 
1-3-5 into as many spaces as there are spaces in 10-8' and 8-6. From the points in 
the various profiles, perpendicular lines are drawn as shown, and solid and dotted lines 
drawn in the usual manner. Diagrams D and E show the true lengths of the solid 
and dotted lines respectively. See similar reference figures. For example: To obtain 
the true length of the dotted line 4'-6 in C, place the length of that line on the hori- 
zontal line in E, shown from 4' to 6 ; from 4' erect the perpendicular 4'-4 equal to 4'-4 
in the profile in C. As point 6 in C has no height, draw a line from 4 to 6 in E, which 
is the true length desired. Proceed in similar manner for the true lengths shown in 



TEXT BOOK ON PATTERN DRAFTING 



149 



D and E. As both prongs A and B are similar, only the pattern shown by F is re- 
quired. Assuming that the seam is to come on i-io in C, the pattern is developed 
as follows: Take the distance 5-6 and place it on 5-6 in F; with 5-4 in C as radius, 
and 5 in F as center, draw the arc 4, which intersect by an arc struck from 6 as center, 
with 6-4 in E as radius. Now, with 6-7 in C as radius, and 6 in F as center, draw 
the arc 7, which intersect by an arc struck from 4 as center, and 4-7 in D as radius. 
Proceed in this manner until the line 3-8 is obtained. Then using S'-p in C as radius 
and 8 in F as center, draw the arc 9, which intersect by its proper radius found in E\ 
then use the spaces in 1-5 in C, and the proper length in D, until the line i-io in F is 
drawn, which is obtained from i-io in C. No matter what profiles the prong may 
have or in what positions the prongs are placed, the foregoing rule holds good. More 
spaces should be used in dividing the profiles, when enlarging this and the various prob- 
lems which will follow. 

FIG. 199. Shows a prong from round to oblong. Both prongs are equal and the 
pattern for either .4 or B only is needed. The tme half section on c~o' is shown by 




(E 4X) 



Fig. 199, 



c-a'-b' ; the distance a'-h' being obtained from a-b. The true half section, and the 
shaded profiles C and D are used when developing the pattern. 

FIGS. 200 and 201. In similar manner develop the patterns for a two-pronged fork, 
the base being a rectangle and the opening of one prong being round and the other 



ISO THE NEW YORK TRADE SCHOOL'S 

square, each prong having a different angle as shown in Fig. 200. A' shows the true 
half section on a~b\ the distance b'-c' being obtained from be. The shaded profiles 
show the parts to be used when developing the arms .4 and B, which are reproduced 
by A and B in Fig. 201 to show how the shaded profiles in Fig. 200 are placed in posi- 
tion in Fig. 201. Note how the profiles are spaced and the solid and dotted lines 
drawn. Develop the pattern for each arm. 





Fig. 201. 



PATTERNS FOR TWO - PIECED TAPERING FORK, 
PARALLEL PIPES AT ANY ANGLE 



MITERING WITH 



FIG. 202. Shows how the patterns are developed when the prongs are mitered 
to horizontal or vertical pipes. ABCD is the elevation of the prong, the base being 
round, the prong C mitering with the horizontal pipe D, and prong B mitering with the 
vertical pipe A. The true section on HJ is obtained the same as in Fig. 198, but the 
true sections on the miter lines 1-5 and 6-10 are obtained as follows: Divide the 
profile F in equal parts as shown, from which parallel to the lines of the pipe D draw 
lines intersecting the Hne 1-5, at i, 2, 3, 4 and 5. From these points at right angle 
to 1-5 erect lines equal in height to similar numbered lines in F, measuring from the 
line 1-5. Through the points 1-2' -t,' -4' and 5, trace the semi-elliptical section shown 
shaded by A^, which is the half true section on 1-5. In similar manner obtain L. Hav- 
ing the true half section on the line 1-5 shown by N, the true half section on HJ shown 
by R, the true half section on the line 6-10 shown by L, and the quarter section P, the 
true lengths of the solid and dotted lines (not here shown) and the patterns for B and 
C are to be obtained in precisely the same manner as described in connection with C 
in Fig. 198. Care must be taken in enlarging this problem that the half profiles L and 
A'' are each divided into as many spaces as are contained in the profiles R and P. The 
pattern for the pipe D is laid off on a-b, and the pattern for A, laid off on cd. The pat- 



TEXT BOOK ON PATTERN DRAFTING 



151 



terns for B and C are to be developed, and when completed will form a fork as shown 
in elevation. Or, two prongs Hke C could be joined, making a fork shown by C°C°, or 
two of B joined, making a fork shown by B°B°. 




Fig. 202 



FIG. 203. Develop the patterns for a fork as shown in Fig. 203, the base being a 
rectangle, the opening of one prong round and the opening of the other square. The 
patterns for the parallel pipes are laid off on a-b and c~d. The true sections on the 
miter lines are obtained as in the preceding problem, and the true section on the seam 
line ea' obtained, by taking the distance ah and placing it as shown by a'b'. At 
pleasure obtain the desired section, which can be drawn as shown by e-f~b'-a' , or 
as shown by eb'a' , or a straight line can be drawn from c to h' . It is immaterial what 
shaped section is placed on e-a' , providing the distance of a'b' is equal to one-half 
of the width of the base as shown by a-h. 



IS2 



THE NEW YORK TRADE SCHOOL'S 




1 
1 

1 


1 

1 
1 

— i- 

1 
1 

PROFILE I 



(E4X) 



b 

Fig. 203. 



PATTERN FOR A THREE - PIECED TAPERING FORK 

FIG. 204. Shows the principle required in developing forks which contain three 
or more prongs. This same principle is applicable whether the prongs pitch at the 
same angle or not, or whether one prong is round and the other square. In this prob- 
lem we have three prongs all having the same angles and diameters, so that the pattern 
for one will answer for all. In laying out the drawing it is only necessary that one 
prong be drawn at right angle to its center line I'B in plan, as shown by i-4'-7'-8-i4. 
This rule applies to any number of prongs. First draw the profile of the base, as shown 
in plan by A-4"-Y. As three prongs are required, divide the circle into three equal 
parts and draw the joint or miter lines A-i', 4"-i' and Y-i'. From 1' erect the line 
I'-i and establish at pleasure the height a~i. From 4' erect the line 4'-4 and at 
pleasure draw the curve 1-4. Then i-a-4 represents the true section on i'-^' in plan. 
Divide this section into equal parts as shown, and from these points drop vertical lines, 
cutting the miter line i'-4' at 2' and 3'. With i' as center and radii equal to 2' and 
3' transfer these points to the miter line i'-4", as shown by 2" and 3". From these 
intersections erect lines, which are intersected by lines drawn from similar numbers 
in the section 1-4, parallel to the base line 4-7', thus obtaining the intersections 2', 
3' and 4'. The curved line 1-4' is then the foreshortened miter line shown in plan 
by i'-4". Now divide the distance from 4" to 7 in plan in equal parts, as shown by 



TEXT BOOK ON PATTERN DRAFTING 



153 



TRUE LENGTHS OF SOLID 
LINES IN D 




TRUE LENGTHS 

OF DOTTED LINES 

IN D 




Fig. 204. 



154 



THE NEW YORK TRADE SCHOOL'S 



4", 5, 6 and 7, and erect lines cutting the base line of the fork at 4', 5', 6' and 7'. C 
represents the profile of the upper opening of one prong. One-half of this is placed in 
position, as shown on the line 8-14, and the semi-circle divided into as many spaces 
as there are divisions in the section 1-4 and in the part plan 7-4" or six spaces. 
Number these spaces as shown from 8 to 14 and draw perpendiculars to the line 8-14 
as shown. Now draw solid and dotted lines in D as shown, and obtain their true lengths 
as shown in diagrams E and F respectively. For example: To find the true length of 
the solid line 3'-! 2', place this distance as shown from 3' to 12' in E, from which erect 
the perpendicular 3'-3" and i2'-i2 equal respectively to the distances measured from 
the line AB in plan to the point 3" and from the line 8-14 in D to the point 12. The 



ELEVATION OF 
ONE PRONG 



TRUE SECTION 
THROUQH 0-'- 




h-'>~->j 




Fig. 206. 



Fig. 205. 



distance from 3" to 12 in £ is then the true length of 3'-! 2' in D. Having found the 
true lengths shown in E and F by similar reference letters, the pattern is developed 
as is shown in H. 7-8 and 1-14 are equal to 7-8 and 1-14 in D. The divisions from 
8 to 14 in // are obtained from the semi-profile in D. The divisions from i to 4 in H 
are obtained from i to 4 in the section i-a-4, while the divisions from 4 to 7 in H 



TEXT BOOK ON PATTERN DRAFTING 



155 



are taken from the spaces 4" to 7 in plan. The opposite half of the pattern is traced 
as shown by 8-i4'-i'-4'-7. 

FIGS. 205, 206 and 207. Develop the pattern for a four-pronged fork, the plan 
of which is shown in Fig. 205. The four prongs being equal, only one pattern is re- 
quired. -4 shows the elevation of one prong, and B the true section through the miter 
line c-e in plan. This true section B, as explained in the preceding problem, can be 
drawn at pleasure after knowing the heiglit n-i and making the distance n-^ equal to 

HALF 
SECTION 




Fig. 207. 



any one of the miter lines in plan as c-e. The half section is placed on 8-14 as shown. 
Note that the foreshortened miter line 1-4' in A is obtained by dropping vertical lines 
from B to the center line a-b in plan, which are then projected to the miter line c-e, 
from which vertical lines are erected, resulting in 1-4'. To show how this same prin- 



i.s6 THE NEW YORK TRADE SCHOOLVS 

ciple can be applied to unequal prongs projecting at various angles and having different 
profiles, Fig. 207 has been prepared. Each of the three prongs must be developed 
separately. Fig. 206 gives a better idea of what we intend to work out in Fig. 207. 
Let A, B and C in Fig. 206 represent a three-pronged fork each projecting at a different 
angle, joining a base of 20 inches diameter, one prong to be 6 inches diameter, the other 
8 inches and the other 5 by 6 inches rectangular. The plan D in Fig. 207 is first drawn 
and divided in the usual manner as shown. After obtaining the true section E and 
the foreshortened miter line a-b, the prong ,4 is drawn at the desired angle, and the 
half section H placed in position, and the pattern for this prong obtained in the same 
manner, as if all the prongs were to be the same as A. Now using the same miter line 
a-b-c, the prong B is drawn at its proper angle, placing the half section G of the rec- 
tangle in the position shown, and the various lines drawn in B as shown, and the pattern 
also developed as if the three prongs were to be similar to B. Finally the prong C 
is drawn with the semi-profile F, as before. Thus it will be seen that the miter lines 
ab and be remain the same, no matter what angle or profile the prong may have. 



PATTERN FOR SHIP VENTILATOR 

FIGS. 208 and 209. Illustrates how the patterns are developed for a ship ventilator, 
or any other form of tapering elbow making a transition from one profile to another. 
First draw the outline of the ventilator, shown by AKLB. The curve LB is struck from 
R and the curve AK from P. KLMN is a straight piece of pipe having profile as 
shown by G. The section or opening on AB is shown by the elliptical profile STVU 
in the front elevation and is drawn by using the rule given in Fig. 8, Part One. Com- 
plete the side elevation of the elbow by dividing the curves AK and BL both into the 
same number of spaces as shown, and draw the miter lines CD, EF and HJ. Bisect 
AB, CD, EF, HJ and KL and obtain a, b, c, d and e. Next complete the front eleva- 
tion by setting off on either side of the center line 511"', the distance WM° and WN°, 
equal to jM and fN in side elevation. Using A' as center, draw the arc TN° in front 
view, also the arc UM°. The distance between these arcs are used for obtaining the 
minor axis of the elliptical sections on the various miter lines in side elevation. It 
should be tmderstood that the arc TN° can be drawn at pleasure, but when once drawn 
it remains a fixed line. Having drawn the front and side elevations, the method of 
finding the various sections on the various miter lines is illustrated in connection with 
Fig. 209, in which 1-7-8-14 is a reproduction of ABCD in Fig. 208. Take a tracing 
of the half section SUV in Fig. 208 and place it as shown by 1-4-7 ii'' Fig. 209. From 
the various points a-b-c-d and e in Fig. 208 draw horizontal lines into the front view, 
cutting the curved lines on both sides at a'-b'-d-d' and e' . b on DC is represented 



TEXT BOOK ON PATTERN DRAFTING 



157 



in Fig. 209 by 11'. From this point at right angle to 8-14 draw the hne ii'-ii, equal 
to one-half the width of b'b' in Fig. 208. Using the rule given in Fig. 8, Part One, 
draw the semi-elliptical section in Fig. 209. Divide both half sections into equal spaces 




FRONT ELEVATION 



Fli;. J08. 



as shown from i to 7 and 8 to 14. From these points erect perpendiculars as shown, 
and draw the solid and dotted lines in the usual manner. These lines then represent 
the bases of sections which must be constructed, the altitudes of which are equal to 
the various heights in the half profiles, in the same manner as the sections and pat- 




FiG. 209. 



terns were developed for the articles given in Figs. 171, 178 and 180. Develop the half 
pattern for each of the four pieces in Fig. 208, obtaining the true profiles on EF and 



158 



THE NEW YORK TRADE SCHOOL'S 



HJ, as explained in Fig. 209. Using the same size side elevation as in Fig. 208, develop 
the half patterns only, for a ventilator or elbow, round to round, as shown in front 
elevation by A°B°C°D°. The curved lines D°E° and E°B° are struck with a radius 
equal to Yn. 



PATTERN FOR TRANSITION PIECE BETWEEN TWO ELBOWS AND VER- 
TICAL PIPE 

FIGS. 210 and 211. In the former figure X shows the elevation of a five-pieced 
elbow, three pieces of which sls A, B and C are to be joined to a transition piece, as 
shown in Fig. 211, in which both portions of the elbow are indicated hy A, B and C, 
the profile of the elbow being shown by D and D. The transition piece for which 




the pattern is required, is shown by F, G, H, J, K, the profile on JH being indicated 
by E. The patterns for the elbows need not be developed, as this was clearly explained 
in Part One. Before proceeding with the pattern for the transition piece, a true sec- 
tion on the miter line FG must be obtained. This is done by dividing the profile D 



TEXT BOOK ON PATTERN DRAFTING 



159 



into equal spaces, as shown from i to 5, from which points Hnes are carried parallel to 
the lines of the elbow as shown, until they intersect the miter line FG. From these 
points at right angle to FG draw the lines 2-3 and 4, equal to like numbered heights 
in D, measuring from the line 1-5. The shaded portion L then represents the true 
section on FG. To avoid a confusion of lines, take a tracing of the transition piece 
and place it as shown in Fig. 210. Now take a tracing of L in Fig. 211 with the var- 
ious points of intersections on same, also a tracing of the semi-profile E, and place them 
as shown by L, L and E in Fig. 210. Divide the profile L into equal spaces, and one- 
half of the semi-profile E into the same number of parts, as shown from i to 5 in L 
and 6 to 10 in £. Draw perpendiculars in the usual manner, then the solid and dotted 
lines as shown. As both halves L and L are symmetrical, it will only be necessary to 
develop the half pattern with seam, as shown. The true lengths of the various solid 
and dotted lines are now obtained and the pattern developed in precisely the same 
manner as explained in connection with Fig. 198. 




^ / 


\ iT 










I / 


\ 


/ 


\ 
\ 


/ 




' 





Jl 



-\ (E4X) 



t 



'M'm,', 



',..,/'.„///,/.. M.,/.m 



PROFILE 

Fig. 212. 



FIG. 212. The method given in the preceding problem is applicable to any similar 
shape or form, as will be seen in the problem now taken up, and in which two elbows 
of unequal size are to be joined to a rectangular transition piece, as shown in Fig. 212. 
The elbow ABC is similar to ABC in Fig. 210, and the elbow ahc in Fig. 212, similar 
to ahc in Fig. 210. E in Fig. 212 is the profile of the large elbow, and D the profile 
of the smaller one. F shows the true profile on JK. In developing the half pattern, 
have the seam come on LK and Jl. True sections must be found on the miter lines HI 
and HL, and the half profile of F must be placed on JK, as shown by the shaded 



i6o THE NEW YORK TRADE SCHOOL'S 

portion; then following the same rule as in Fig. 210, the true lengths and pattern are 
obtained. 



PATTERN FOR IRREGULAR T-JOINT 

FIG. 213. In enlarging this problem, more spaces should be used in the profile C than 
appear in the illustration. This problem shows the intersection between a transition 
pipe whose vertical profile on 5°-6° is shown by B, intersecting a vertical cylinder D, the 
profile of which is indicated by C. While a plan view is shown, it is not necessary in the 
development of the pattern when both halves are symmetrical. After the outline of the T 
is drawn, bisect the angle t°~i'-d as shown by cde, and draw the line e-\' until it inter- 
sects the center line of the vertical pipe at 3', from which draw a line to 1°. Now divide 
the semi-profile C in equal parts, as shown from i to 3 on both sides, and erect lines, cut- 
ting the lines i'-3'-i° at i', 2', 3', 2° and 1°. For the opening cut in the vertical pipe, 
take the stretchout of the semi-profile C and place it on a-h. Erect perpendiculars 
as shown, which intersect by horizontal lines drawn from similar numbered intersection 
in D, resulting in the points of intersections shown by i^, 2'', 3^, 2" and i" in the 
pattern. The shaded portion shows the developed opening. From the various inter- 
sections 2' and 3' in 5 draw lines to 6°, and from the intersections 3' and 2° in R draw 
lines to 5°. These lines then represent the bases of sections having altitudes equal 
to the heights in the semi-profiles B and C. 5°-i° and 6°-i' show their true lengths. 
To find the true length of s°-3', place this distance as shown by 5°-3' in E\ draw the 
perpendiculars 5°-5 and 3'-3 equal in height to 5'-5 in B and one-half of 'i,--i, in C. 
Then 3-5 in R shows the true length of 3'-5° in R. E shows the true lengths of the 
lines in R, and F the true lengths of the lines in 5. The half pattern is shown developed 
by T. The distances s'-i^ and 6'-i^ are obtained from 5°-i° in R and 6°-i' in 5 
respectively. The distances $'-5, 5-6 and 6-6' in T, are obtained from the semi-profile 
B\ the true lengths in T, from the diagrams E and F, and the divisions from i^ to i" 
in T from similar divisions in the pattern for the opening in the vertical pipe, all as 
shown by similar reference figures. 

FIG. 214. Develop the pattern for the opening in the vertical pipe A in Fig. 
214, when intersected by the transition piece C, laying off the pattern on cd. Also 
develop the pattern for C. B is the profile for A, and D the profile of the opening 
in the transition piece C. The true lengths are found by using the solid and dotted 
line in C as base lines, and the heights on one side of the center line ab in both D and 
B as altitudes, as shown by similar figures. 



TEXT BOOK ON PATTERN DRAFTING 



i6i 




Fig. 213. 



Fi.;. 21.1. 



i62 THE NEW YORK TRADE SCHOOL'S 



PATTERN FOR IRREGULAR TRANSITION PIECE, INTERSECTING HORI- 
ZONTAL CYLINDER 

FIG. 215. The principles shown in Fig. 215 are applicable to any irregular tran- 
sition piece such as is here shown, no matter whether the outline is diamond-shape, 
round or elliptical. The problem here shown represents a diamond boss mitering against 
a cylinder whose profile is partly shown by AB and is struck from the center C. The 
side elevation of the boss is shown by 5°-5°-4°-4°. 5-8'-5'-8 represents the plan view 
on 5°-5° in elevation, and i-4-i'-4' the plan view on 4°-4° in elevation. As the four 
quarters in plan view are alike, it will only be necessary to develop one-quarter, then 
join two of these to make a half pattern with seams as shown in plan. Therefore divide 
the quarter circle in plan into equal spaces, as shown from i to 4, which points are 
represented in elevation on the plane 4°-4°, as shown by i°-2°-3° and 4°. In similar 
manner divide part of the curve 5° to 8° also into four parts as in P, as shown by 
5°-6°-7° and 8°, from which points drop vertical lines intersecting 5-8 in plan at 5-6-7 
and 8. SoHd and dotted lines are now drawn in plan, which represent respectively 
the bases of triangles which will be constructed with altitudes equal to the various 
heights in the side elevation. For example: The true distance of 3-6 in plan is found 
by placing this distance as shown by 3-6 in R. From 6 the vertical line 6-6 is erected, 
equal to the vertical height from the line 4°-4° in side elevation to the point 6°. The 
hypotenuse 6-3 in R then represents the true length of 6-3 in plan. In this manner 
the true distances of the solid lines in R and the dotted lines in 5 are obtained. The 
distance along 5-8 in plan does not show its true length because the line 5°-8° in 
elevation does not lie on a horizontal plane. Therefore this true length on 5°-8° in 
elevation or, what is the same, 5-8 in plan is obtained as follows : Take the various 
points of intersections on 5°-8° in elevation and place them on the line 5 '-5 extended 
in plan, as shown by similar numbers 5° to 8''. From these points erect perpendiculars, 
which are intersected by horizontal lines drawn from similar numbered intersections 
in plan, resulting in 5°-6°-7° and 8° in T, which represents the true length desired. 
8o_jO_gv aigQ represents the quarter opening in cylinder. Having found the necessary 
true lengths the one-quarter pattern is developed as shown in W. The distances of 
the soHd lines are taken from /?; the distances of the dotted lines from 5; the various 
divisions i to 4 in W are obtained from i tn 4 in plan, while the various divisions 
from 5 to 8 in W are obtained from 5° to 8° in T. Trace the quarter pattern oppo- 
site the line 1-8 in W, then 5-5'-4'-4 will be the half pattern, with seams as shown 
in plan. Develop the half pattern for an irregular transition piece. The section or 
I^irofile on the line 4°-4° will be the same as P in plan, but the lower outline will be an 



TEXT BOOK ON PATTERN DRAFTING 



163 



ellipse having a major axis equal to 5-5' in plan, and a minor axis equal to 8-8' ; 
this ellipse to represent a horizontal section on the angle 5°r5° in elevation, against 
which it is to miter in place of the curve A-?>°-B. Use the same size drawing as before, 
only changing to the angle in elevation and to the ellipse in plan. 




TRUE LENGTH OF THE 

CURVED LIME a'-'-:,-' 

in elevation, 

os one quarter opening 

in cylincer 

Fig. 215. 



PATTERN FOR A BATH TUB 

FIG. 216. The principles in this problem are similar to those shown in Fig. 215, only 
the operations will be reversed when obtaining the true lengths of the solid and dotted 
hnes in the diagrams H and J in Fig. 216. In other words, instead of using the plan 
for obtaining the bases, and the elevation for obtaining the altitudes, as was done in Fig. 
215, we will now use in Fig. 216 the lines in elevation as the bases, and the various 
half distances in the horizontal sections as the altitudes, as hereafter explained. What 



i64 THE NEW YORK TRADE SCHOOL'S 

method to employ is left to the judgment of the pattern cutter. First draw the 
elevation of the tub as shown by C. In its proper position draw the horizontal section 
on 1-7 in elevation as shown by A, the semi-circles being struck from a and b, and 
the straight lines drawn tangent to them. In similar manner, in its proper position, 
draw the horizontal section on I'-j' in elevation, as shown by B, the semi-circles being 
struck from d and e, and the straight lines drawn tangent to them. Now divide the 
curves in the half profile .4 into equal spaces, as shown from i to 3 and 4 to 7, from 
which erect vertical lines intersecting the base lines 1-7 in C, as shown by similar num- 
bers. In similar manner divide the curves in the half profile B into the same number 
of spaces, as shown from i' to 3' and 4' to 7', from which points lines are dropped cut- 
ting the outline i'~y' in C, as shown by similar numbers. The curved outline 3' to 4' 
in C is now divided into equal parts, as shown by S'-g' and 10', from which lines are 
erected to the section B, intersecting same at S'-g' and 10'. Solid and dotted lines 
are now drawn in the elevation C, as shown, which represent the bases of the sections 
to be constructed, and which are shown in diagrams H and J. Thus the true length 
of the dotted line 4'-s in elevation is obtained by placing this distance on the hori- 
zontal line in '}', as shown by 4'-5, then erecting the perpendiculars 4'-4' and 5-5, 
equal to similar numbered distances measured from the line I'-j' in B, to the point 
4', and from the line 1-7 in A to the point 5 respectively. The slanting line 4'-5 in 
J then represents the true length of 4'-5 in C. As the line I'-j' in C does not lie on 
a horizontal plane, then B does not show the developed section, the same as A does 
on the line 1-7 in C. To find this developed section on I'-j' in C, take the various 
divisions on this curved line and place them on the line de extended in B, as shown 
by similar figures i" to 7" on FE. From the various divisions i" to 7" drop per- 
pendicular lines, which intersect by horizontal lines drawn from similar numbered 
intersection in B, resulting in the intersections 2° to 6° in D. A line traced through 
these points is the half developed section through I'-f in C. Having the various 
true lengths, the half pattern is developed as shown in diagram M, in which the solid 
lines are obtained from H, the dotted lines from 7, the divisions from i to 7 in M are 
obtained from A, and the divisions from i' to 7' in M from D. i-i' and 7-7' in M 
are obtained respectively from i-i' and 7-7' in C, on which lines the seam is located. 
Use the same size drawing as in Fig. 216 and obtain the half pattern for a bath tub, 
when the top has a slant line as shown by the dotted line from i' to 7' in C. 



TEXT BOOK ON PATTERN DRAFTING 



165 




y' 


- 


lU' 


i' 


H 


6' 

6 



TRUE LENGTHS OF DOTTED LINES 
IN C 




one half pattern 
Fig. 216. 



i66 THE NEW YORK TRADE SCHOOL'S 



PATTERN FOR A FUNNEL COAL HOD 

FIG. 217. Shows how the pattern is obtained for a funnel coal hod. The prin- 
ciples in this problem do not differ from those given in the preceding problem. The 
side elevation A is first drawn, then the horizontal section on 6'-io' placed in its proper 
position as shown by B. In similar manner the section C is placed in line with I'-s'. 
A horizontal section on the curved line ii'-is' is now constructed as shown by D, in 
which a is the center of the semi-circle b-ii-b; b the center of the arc bi, and c the 
center of the arc i-i. Each of the semi-sections B, C, D are divided into the same 
number of spaces, and perpendiculars drawn until they cut the various section lines in 
elevation, as shown by similar reference figures. Note how the solid lines in elevation 
are drawn, also the dotted lines connecting opposite points. These solid and dotted 
lines represent the bases of sections, the altitudes of which equal the distances in the 
various semi-sections in B, C and D respectively, as shown by similar reference figures 
in the diagrams J and L, which represent respectively the tioie lengths of the solid 
and dotted lines in A. A developed section must now be found on ii'-i5' in A as 
shown by E. Take the girth of ii'-is' in A, and place it on the center line in D ex- 
tended as shown in E. Draw perpendiculars as shown, which intersect by horizontal 
lines drawn from similar numbers in D as 11, 12°, 13°, 14° and 15 in E. A line 
traced through these intersections will give the half developed section on ii'-i5' in A. 
Having found the various true lengths, the pattern is developed as shown in M, in 
which the distances 5-6, lo-ii and 15-1 are obtained respectively from 5'-6', lo'-ii' 
and is'-i' in A. The divisions from 5 to i in M are obtained from the semi-section 
C ; the divisions from 15 to 11 in M from the half developed section E ; the divisions 
from 6 to 10 in M from the semi-section B, and the lengths of the various solid and 
dotted lines in M from the slant lines in the diagrams J and L. i, 5, 6, 10, 11, 15 
in M is then the half pattern for the hod A, with seams at i'-i5', 5'-6' and lo'-ii'. 
If a full pattern is desired with seams at top I'-is' and back lo'-ii', it is only necessary 
to trace the half pattern in M opposite the line 5-6, as shown by I'-is'-ii' and 10'. 
H is the pattern for the foot F. 

FIGS. 218 and 219. Solve the problem shown in Fig. 219, a perspective of which 
is shown in Fig. 218, being an open top coal hod. A in Fig. 219 shows the side eleva- 
tion of the hod, B the true section on i'-5', and C the horizontal section on 6'-io'. 
a is the center of B, and b the center from which the semi-circle in C is struck. Divide 
both the semi-sections in the same number of spaces as shown ; obtain the various 
intersections in elevation, and draw the solid and dotted lines in the usual manner. 
The true lengths of the solid and dotted lines are obtained, by using the various solid 



TEXT BOOK ON PATTERN DRAFTING 



167 



HORIZONTAL SECTION ON II-I5' 



HALF DEVELOPED SECTION 
ON 11-15' IN ELEVATION 



SECTION ON 

r-5' 




TRUE LENGTHS OF 
SOLID LINES IN A 



TRUE LENGTHS OF 
DOTTED LINES IN A 



1 FULL PATTERN j' 




Fig. 217. 



i68 



THE NEW YORK TRADE SCHOOL'S 



and dotted lines in A as bases, and the various distances in the semi-sections as 
altitudes in precisely the same manner as was done in Fig. 217. The developed sec- 
tion on 6'- 10' in Fig. 219 is obtained in similar manner as E was obtained in Fig. 217. 



HORIZONTAL SECTION 
ON 6-10' 





SIDI 
ELEVATION 



Fig. 218. 



Fig. 219. 



Develop the pattern for the hod in Fig. 219 in one piece with a seam on 5'-6' in side 
elevation. Also develop the pattern for the foot D. n shows the center from which 
the pattern is struck, the pattern being obtained as shown in diagram H in Fig. 217. 
In enlarging the problem in Fig. 219 double the amount of spaces should be used in 
the sections B and C. 



TEXT BOOK ON PATTERN DRAFTING 169 



CONCLUSION 

The variety of forms arising in sheet metal work is practically iinlimited, and many 
more problems could be furnished. But the principles involved would simply be a 
repetition of what has already been explained. The course of instruction in which 
this textbook is used, imparts the basic principles of pattern drafting. Having 
once mastered the principles, the student should experience no difficulty in preparing 
patterns for any of the various forms he may encounter in practice. 





!li ! 



'ill 






,1 



li! 'i'li ! 



